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This document discusses methods for computing the area and volume of surveyed land. It describes several rules that can be used to calculate area based on the shape and accuracy needs, including mid-ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's one-third rule. The trapezoidal and prismoidal rules are presented for calculating volume from cross-sectional areas. The most accurate methods involve subdividing irregular boundaries into geometric shapes or using a planimeter for highly irregular boundaries.

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2021031026 S GOPAL SWE.pptx

This document discusses methods for computing the area and volumes of surveyed land. It describes several rules that can be used to calculate area, including the mid ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's one-third rule. These rules make assumptions about the shape of boundaries and can be used with varying levels of accuracy. The document also outlines the trapezoidal rule and prismoidal rule for computing volumes of earthwork based on calculating cross-sectional areas.

ppt ofcalculation of area and volume.pptx

For civil engineering

Area & volume 3

1. There are several methods to calculate the area of land from survey data, including graphical, instrumental, and from field notes.
2. Common units for expressing area include square meters, hectares, square feet, and acres.
3. Key computational methods covered are the mid-ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's rule, which involve calculating the area based on ordinates or offsets taken at regular intervals along a baseline.
4. Each method makes different assumptions about the shape of the boundary between ordinates, with Simpson's rule assuming a parabolic arc to provide a more accurate result than the trapezoidal rule.

5. AREAS AND VOLUMES (SUR) 3140601 GTU

Introduction, computation of area, computation of area from field notes and plotted plans, boundary area, area of traverse, Use of Plannimeter, computations of volumes, Volume from cross sections, Trapezoidal and Prismoidal formulae, Prismoidal correction, Curvature correction, capacity of reservoir, volume from borrow pits.

Lecture 17 M4.pdf

1) Several methods are described for calculating the area of land from surveying data, including graphical, instrumental, and computational methods using field notes.
2) Computational methods include dividing the land into geometric shapes and calculating the area of each shape. Common shapes are triangles, squares, rectangles, and trapezoids.
3) Areas can be calculated from plotted plans using methods like dividing the land into triangles and calculating each triangle's area, or dividing the land into squares of equal size and counting the number of squares.

Area & Volume

This document discusses various methods for computing the area of irregular shapes from field notes and plotted plans in surveying. It describes graphical, instrumental, and computational methods using the trapezoidal rule, mid-ordinate rule, average ordinate rule, and Simpson's rule. Specific steps are outlined for computing area from field notes by dividing the shape into triangles, rectangles, squares, and trapezoids. Methods for computing area from a plotted plan include dividing the shape into triangles using bases and altitudes, counting squares of a known unit area, or drawing parallel lines to form rectangles.

unit-3.ppt

This document discusses different methods for computing the area and volume of land surfaces in civil engineering. It provides formulas for calculating areas using the mid-ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's rule based on taking offset measurements. It also describes calculating cross-sectional areas of surfaces using formulas for level sections, two-level sections, three-level sections, side hill two-level sections, and multi-level sections. The document states that volume is calculated using the trapezoidal rule or prismoidal rule, and the prismoidal rule is more accurate by applying a correction.

Simpson_rule_And_Trapezoidal_Rule.pptx

This document discusses methods for calculating areas and volumes in surveying, including the trapezoidal rule and Simpson's rule. It provides examples of using these rules to calculate the area between an irregular boundary line and a chain line using offsets taken at regular intervals. It also discusses calculating volumes using prismoidal and trapezoidal rules, providing an example of calculating the cost of earth work for constructing a farm pond based on its dimensions.

2021031026 S GOPAL SWE.pptx

This document discusses methods for computing the area and volumes of surveyed land. It describes several rules that can be used to calculate area, including the mid ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's one-third rule. These rules make assumptions about the shape of boundaries and can be used with varying levels of accuracy. The document also outlines the trapezoidal rule and prismoidal rule for computing volumes of earthwork based on calculating cross-sectional areas.

ppt ofcalculation of area and volume.pptx

For civil engineering

Area & volume 3

1. There are several methods to calculate the area of land from survey data, including graphical, instrumental, and from field notes.
2. Common units for expressing area include square meters, hectares, square feet, and acres.
3. Key computational methods covered are the mid-ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's rule, which involve calculating the area based on ordinates or offsets taken at regular intervals along a baseline.
4. Each method makes different assumptions about the shape of the boundary between ordinates, with Simpson's rule assuming a parabolic arc to provide a more accurate result than the trapezoidal rule.

5. AREAS AND VOLUMES (SUR) 3140601 GTU

Introduction, computation of area, computation of area from field notes and plotted plans, boundary area, area of traverse, Use of Plannimeter, computations of volumes, Volume from cross sections, Trapezoidal and Prismoidal formulae, Prismoidal correction, Curvature correction, capacity of reservoir, volume from borrow pits.

Lecture 17 M4.pdf

1) Several methods are described for calculating the area of land from surveying data, including graphical, instrumental, and computational methods using field notes.
2) Computational methods include dividing the land into geometric shapes and calculating the area of each shape. Common shapes are triangles, squares, rectangles, and trapezoids.
3) Areas can be calculated from plotted plans using methods like dividing the land into triangles and calculating each triangle's area, or dividing the land into squares of equal size and counting the number of squares.

Area & Volume

This document discusses various methods for computing the area of irregular shapes from field notes and plotted plans in surveying. It describes graphical, instrumental, and computational methods using the trapezoidal rule, mid-ordinate rule, average ordinate rule, and Simpson's rule. Specific steps are outlined for computing area from field notes by dividing the shape into triangles, rectangles, squares, and trapezoids. Methods for computing area from a plotted plan include dividing the shape into triangles using bases and altitudes, counting squares of a known unit area, or drawing parallel lines to form rectangles.

unit-3.ppt

This document discusses different methods for computing the area and volume of land surfaces in civil engineering. It provides formulas for calculating areas using the mid-ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's rule based on taking offset measurements. It also describes calculating cross-sectional areas of surfaces using formulas for level sections, two-level sections, three-level sections, side hill two-level sections, and multi-level sections. The document states that volume is calculated using the trapezoidal rule or prismoidal rule, and the prismoidal rule is more accurate by applying a correction.

Simpson_rule_And_Trapezoidal_Rule.pptx

This document discusses methods for calculating areas and volumes in surveying, including the trapezoidal rule and Simpson's rule. It provides examples of using these rules to calculate the area between an irregular boundary line and a chain line using offsets taken at regular intervals. It also discusses calculating volumes using prismoidal and trapezoidal rules, providing an example of calculating the cost of earth work for constructing a farm pond based on its dimensions.

Area & volume 2

The document discusses methods for calculating area and volume. It begins by defining the objectives as explaining the basic concepts of area and volume, describing common usage, and outlining methods used in calculations. Several geometric formulas are provided for calculating the area of rectangles, triangles, trapezoids, and irregular shapes. Methods like the trapezoidal rule, mid-ordinate rule, and Simpson's rule are described for calculating irregular areas using coordinates. The document also discusses calculating cross-sectional areas and volumes using methods like mean area, end area, and prismoidal formulas applied to cross-sections, as well as calculating volumes from spot levels and contour lines. Examples are provided to demonstrate applying the different formulas and methods.

05_chapter 6 area computation.pdf

The document discusses different methods for measuring land area, including:
1. Dividing plots into triangles, rectangles, and trapezoids and using formulas to calculate their individual areas and sum them.
2. Taking offsets from a base line and using average ordinate, trapezoidal, or Simpson's rules to calculate the area between the base line and boundary.
3. The coordinate method, which uses the x and y coordinates of boundary points to calculate the total area of a closed traverse.

Area and volume_Surveying, Civil Engineering

This document outlines methods for computing area and volume from land survey field notes. It discusses several methods to compute area, including the mid ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's one-third rule. These methods can be used to calculate area based on offsets taken in the field or from a plotted plan. It also describes the trapezoidal rule and prismoidal formula for computing cut and fill volumes from cross-sectional areas along a surveyed line.

Chap6_Sec1.ppt

The document discusses using integrals to calculate the area between two curves. It provides examples of finding areas bounded above and below by functions, including cases where the boundary curves intersect and cases where graphical methods are needed to find approximate intersection points. The key formula given is that the area between curves y=f(x) and y=g(x) from x=a to x=b is the integral from a to b of f(x)-g(x) dx. Examples are worked out demonstrating the application of this formula.

Topic 2 area & volume

The document provides information on calculating area and volume for engineering projects. It discusses several methods for calculating the area of regular and irregular shapes, including using mathematical equations, coordinates, planimeters, trapezoidal rule, mid-ordinate rule, and Simpson's rule. It also outlines various approaches to calculating volumes based on cross-sections, spot levels, and contour lines, including end area method, mean area method, and prismoidal formula. Examples are provided to demonstrate calculating area and volume using these different techniques.

Area_Contour.ppt

This document discusses methods for determining land areas through surveying and calculating contours. It provides three main methods for computing areas: (1) dividing the area into triangles and calculating each triangle's area, (2) measuring offsets between survey lines and boundaries and using trapezoidal or Simpson's rules to calculate areas, and (3) comparing the trapezoidal and Simpson's rules. It also defines contours as imaginary lines joining points of equal elevation, discusses contour characteristics like spacing and shape that indicate terrain features, and lists uses of contour maps in civil engineering projects.

Computation of area

This document discusses different methods for calculating areas in surveying, including graphical, coordinate, and planimeter methods. The coordinate method is commonly used to calculate irregular areas by splitting them into trapezoids and applying the trapezoidal rule or Simpson's rule formulas. Examples are provided to demonstrate calculating areas using offsets and these rules, along with limitations around applying the rules to datasets with irregular intervals.

Areas and Definite Integrals.ppt

The document discusses how to calculate the area under a curve using definite integrals and the Fundamental Theorem of Calculus. It explains that the area can be approximated as the sum of rectangles and becomes exact as the width approaches zero. The area is then given by the definite integral from a to b of the function, which is equal to evaluating the antiderivative at b and subtracting the evaluation at a. Examples demonstrate calculating areas under parabolic and exponential curves using this process.

HOME ASSIGNMENT (0).pptx

This document discusses various numerical analysis methods for solving differential and partial differential equations. It begins with a brief history of numerical analysis, then discusses different interpolation methods like Lagrangian interpolation. It also covers finite difference methods, finite element methods, spectral methods, and the method of lines - explaining how each method discretizes equations. The document concludes by discussing multigrid methods, which use a hierarchy of grids to accelerate convergence in solving equations.

HOME ASSIGNMENT omar ali.pptx

This document discusses numerical methods for solving differential and partial differential equations. It begins by providing some historical context on the development of numerical analysis. It then discusses several common numerical methods including Lagrangian interpolation, finite difference methods, finite element methods, spectral methods, and finite volume methods. For each method, it provides a brief overview of the approach and discusses aspects like discretization, accuracy, computational cost, and common applications. Overall, the document serves as an introduction to various numerical techniques for approximating solutions to differential equations.

S2 9 areas and volumes

The document discusses two numerical integration methods for approximating the area under a curve:
1) The trapezoidal rule approximates the area as a sum of trapezoidal areas under strips of equal width. It is applied to an example where it estimates the area as 625 square meters.
2) Simpson's rule assumes the boundary is composed of parabolic arcs rather than straight lines, making it more accurate. It is applied to the same example and estimates the area as 584 square meters.

Methods of computation of area in Surveying.ppt

This document discusses several common methods used to compute the area of plots of land or structures in surveying: the mid-ordinate method, average ordinate method, trapezoidal rule, Simpson's rule, and graphical method. Each method uses a different calculation that involves dividing the plot into strips or ordinates and multiplying distances and sums of the ordinates.

Overviewing the techniques of Numerical Integration.pdf

In this presentation we discuss the ways of integrating a function using trapezoidal, simpsons 1/3,3/8 and boole's method. We also discussed its error and analysised other ways to solve it than mention.

Lecture 18 M5.pdf

The dimensions of the sump are:
Lower base diameter = 6m
Upper base diameter = 4m
Height of remaining part = 3m
Area of lower base = πr2 = π(3)2 = 28.26m2
Area of upper base = πr2 = π(2)2 = 12.56m2
Volume of remaining part = Volume of frustum - Volume filled initially
= (1/3) × (Area of lower base + Area of upper base + √(Area of lower base × Area of upper base)) × Height
= (1/3) × (28.26 + 12.56 + √(28.26

Calculate_distance_and_bearing_between Latitude_Longitude_Points.docx

This document provides formulas and code snippets for calculating distances, bearings, and other values between latitude/longitude points. It discusses the haversine formula for calculating great-circle distance, as well as the spherical law of cosines. It also provides formulas and examples for calculating initial and final bearings, midpoints, and intermediate points along a great-circle path between two points.

Calculate_distance_and_bearing_between Latitude_Longitude_Points.docx

This document provides formulas and code snippets for calculating distances, bearings, and other values between latitude/longitude points. It discusses the haversine formula for calculating great-circle distance, as well as the spherical law of cosines. It also provides formulas and examples for calculating initial and final bearings, midpoints, and intermediate points along a great-circle path between two points.

AREA AND PERIMETER

This document defines and provides formulas for calculating the area and perimeter of basic shapes like triangles, squares, rectangles, and parallelograms. It also includes examples of using the formulas to find the area and perimeter of these shapes given specific dimensions. Key formulas included are that the perimeter of a triangle is the sum of its three sides, the area is 1/2 base x height, the perimeter of a square is 4 times the length of a side, and its area is the square of the side length. Formulas for rectangles and parallelograms relate the perimeter to sums of adjacent sides and the area to the product of base and height.

Integration

This document covers several topics related to integration including:
1. The history of calculating areas, from early civilizations knowing formulas for basic shapes to Archimedes pioneering the method of exhaustion to calculate curved regions like circles.
2. The rectangle method, which divides regions into rectangles to estimate their total area, and how taking more rectangles leads to better approximations of exact areas.
3. The relationship between integration and finding areas, where the integral of a function is the area under its curve over an interval and the derivative of the area function is the bounding curve.
4. Properties of indefinite integrals like additivity and the substitution rule for performing integrals of composite functions.

ch6&7.pdf

The document discusses methods for computing land and earthwork areas and volumes. It describes using triangles, trapezoids, offsets and coordinates to calculate irregular plot areas. For volumes, it covers the average end-area and trapezoidal rules to calculate volumes between cross-sections, as well as using spot levels and formulas to determine cut/fill volumes. Formulas are provided for triangular, rectangular and composite land areas and volumes.

Numerical Solution of Diffusion Equation by Finite Difference Method

IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.

pvpresentationfsecmodified-130908085906-.pptx

Photovoltaic (PV) systems convert sunlight directly into electricity and can power various applications where other power sources are impractical or unavailable. PV systems are increasingly popular and have many uses such as providing power for remote telecommunications towers, water pumping, lighting, and powering devices in developing areas that lack electricity infrastructure. PV power is also used for off-shore navigational aids, highway signs, recreational vehicles, and large utility-scale systems.

integratedweedmangement-200730175200.pptx

Integrated Weed Management (IWM) utilizes multiple weed control techniques including blind tillage, mechanical weeders, and herbicides. Blind tillage uproots extra plants and broadleaved weeds after crop planting without damaging young crops. Mechanical weeders like dry land weeders, power rotary weeders, and tractor operated multi row rotary weeders are used to remove shallow rooted and inter row weeds in various row crops. The cono weeder is a manual weeder that efficiently removes weeds between crop rows.

Area & volume 2

The document discusses methods for calculating area and volume. It begins by defining the objectives as explaining the basic concepts of area and volume, describing common usage, and outlining methods used in calculations. Several geometric formulas are provided for calculating the area of rectangles, triangles, trapezoids, and irregular shapes. Methods like the trapezoidal rule, mid-ordinate rule, and Simpson's rule are described for calculating irregular areas using coordinates. The document also discusses calculating cross-sectional areas and volumes using methods like mean area, end area, and prismoidal formulas applied to cross-sections, as well as calculating volumes from spot levels and contour lines. Examples are provided to demonstrate applying the different formulas and methods.

05_chapter 6 area computation.pdf

The document discusses different methods for measuring land area, including:
1. Dividing plots into triangles, rectangles, and trapezoids and using formulas to calculate their individual areas and sum them.
2. Taking offsets from a base line and using average ordinate, trapezoidal, or Simpson's rules to calculate the area between the base line and boundary.
3. The coordinate method, which uses the x and y coordinates of boundary points to calculate the total area of a closed traverse.

Area and volume_Surveying, Civil Engineering

This document outlines methods for computing area and volume from land survey field notes. It discusses several methods to compute area, including the mid ordinate rule, average ordinate rule, trapezoidal rule, and Simpson's one-third rule. These methods can be used to calculate area based on offsets taken in the field or from a plotted plan. It also describes the trapezoidal rule and prismoidal formula for computing cut and fill volumes from cross-sectional areas along a surveyed line.

Chap6_Sec1.ppt

The document discusses using integrals to calculate the area between two curves. It provides examples of finding areas bounded above and below by functions, including cases where the boundary curves intersect and cases where graphical methods are needed to find approximate intersection points. The key formula given is that the area between curves y=f(x) and y=g(x) from x=a to x=b is the integral from a to b of f(x)-g(x) dx. Examples are worked out demonstrating the application of this formula.

Topic 2 area & volume

The document provides information on calculating area and volume for engineering projects. It discusses several methods for calculating the area of regular and irregular shapes, including using mathematical equations, coordinates, planimeters, trapezoidal rule, mid-ordinate rule, and Simpson's rule. It also outlines various approaches to calculating volumes based on cross-sections, spot levels, and contour lines, including end area method, mean area method, and prismoidal formula. Examples are provided to demonstrate calculating area and volume using these different techniques.

Area_Contour.ppt

This document discusses methods for determining land areas through surveying and calculating contours. It provides three main methods for computing areas: (1) dividing the area into triangles and calculating each triangle's area, (2) measuring offsets between survey lines and boundaries and using trapezoidal or Simpson's rules to calculate areas, and (3) comparing the trapezoidal and Simpson's rules. It also defines contours as imaginary lines joining points of equal elevation, discusses contour characteristics like spacing and shape that indicate terrain features, and lists uses of contour maps in civil engineering projects.

Computation of area

This document discusses different methods for calculating areas in surveying, including graphical, coordinate, and planimeter methods. The coordinate method is commonly used to calculate irregular areas by splitting them into trapezoids and applying the trapezoidal rule or Simpson's rule formulas. Examples are provided to demonstrate calculating areas using offsets and these rules, along with limitations around applying the rules to datasets with irregular intervals.

Areas and Definite Integrals.ppt

The document discusses how to calculate the area under a curve using definite integrals and the Fundamental Theorem of Calculus. It explains that the area can be approximated as the sum of rectangles and becomes exact as the width approaches zero. The area is then given by the definite integral from a to b of the function, which is equal to evaluating the antiderivative at b and subtracting the evaluation at a. Examples demonstrate calculating areas under parabolic and exponential curves using this process.

HOME ASSIGNMENT (0).pptx

This document discusses various numerical analysis methods for solving differential and partial differential equations. It begins with a brief history of numerical analysis, then discusses different interpolation methods like Lagrangian interpolation. It also covers finite difference methods, finite element methods, spectral methods, and the method of lines - explaining how each method discretizes equations. The document concludes by discussing multigrid methods, which use a hierarchy of grids to accelerate convergence in solving equations.

HOME ASSIGNMENT omar ali.pptx

This document discusses numerical methods for solving differential and partial differential equations. It begins by providing some historical context on the development of numerical analysis. It then discusses several common numerical methods including Lagrangian interpolation, finite difference methods, finite element methods, spectral methods, and finite volume methods. For each method, it provides a brief overview of the approach and discusses aspects like discretization, accuracy, computational cost, and common applications. Overall, the document serves as an introduction to various numerical techniques for approximating solutions to differential equations.

S2 9 areas and volumes

The document discusses two numerical integration methods for approximating the area under a curve:
1) The trapezoidal rule approximates the area as a sum of trapezoidal areas under strips of equal width. It is applied to an example where it estimates the area as 625 square meters.
2) Simpson's rule assumes the boundary is composed of parabolic arcs rather than straight lines, making it more accurate. It is applied to the same example and estimates the area as 584 square meters.

Methods of computation of area in Surveying.ppt

This document discusses several common methods used to compute the area of plots of land or structures in surveying: the mid-ordinate method, average ordinate method, trapezoidal rule, Simpson's rule, and graphical method. Each method uses a different calculation that involves dividing the plot into strips or ordinates and multiplying distances and sums of the ordinates.

Overviewing the techniques of Numerical Integration.pdf

In this presentation we discuss the ways of integrating a function using trapezoidal, simpsons 1/3,3/8 and boole's method. We also discussed its error and analysised other ways to solve it than mention.

Lecture 18 M5.pdf

The dimensions of the sump are:
Lower base diameter = 6m
Upper base diameter = 4m
Height of remaining part = 3m
Area of lower base = πr2 = π(3)2 = 28.26m2
Area of upper base = πr2 = π(2)2 = 12.56m2
Volume of remaining part = Volume of frustum - Volume filled initially
= (1/3) × (Area of lower base + Area of upper base + √(Area of lower base × Area of upper base)) × Height
= (1/3) × (28.26 + 12.56 + √(28.26

Calculate_distance_and_bearing_between Latitude_Longitude_Points.docx

This document provides formulas and code snippets for calculating distances, bearings, and other values between latitude/longitude points. It discusses the haversine formula for calculating great-circle distance, as well as the spherical law of cosines. It also provides formulas and examples for calculating initial and final bearings, midpoints, and intermediate points along a great-circle path between two points.

AREA AND PERIMETER

This document defines and provides formulas for calculating the area and perimeter of basic shapes like triangles, squares, rectangles, and parallelograms. It also includes examples of using the formulas to find the area and perimeter of these shapes given specific dimensions. Key formulas included are that the perimeter of a triangle is the sum of its three sides, the area is 1/2 base x height, the perimeter of a square is 4 times the length of a side, and its area is the square of the side length. Formulas for rectangles and parallelograms relate the perimeter to sums of adjacent sides and the area to the product of base and height.

Integration

This document covers several topics related to integration including:
1. The history of calculating areas, from early civilizations knowing formulas for basic shapes to Archimedes pioneering the method of exhaustion to calculate curved regions like circles.
2. The rectangle method, which divides regions into rectangles to estimate their total area, and how taking more rectangles leads to better approximations of exact areas.
3. The relationship between integration and finding areas, where the integral of a function is the area under its curve over an interval and the derivative of the area function is the bounding curve.
4. Properties of indefinite integrals like additivity and the substitution rule for performing integrals of composite functions.

ch6&7.pdf

The document discusses methods for computing land and earthwork areas and volumes. It describes using triangles, trapezoids, offsets and coordinates to calculate irregular plot areas. For volumes, it covers the average end-area and trapezoidal rules to calculate volumes between cross-sections, as well as using spot levels and formulas to determine cut/fill volumes. Formulas are provided for triangular, rectangular and composite land areas and volumes.

Numerical Solution of Diffusion Equation by Finite Difference Method

IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.

Area & volume 2

Area & volume 2

05_chapter 6 area computation.pdf

05_chapter 6 area computation.pdf

Area and volume_Surveying, Civil Engineering

Area and volume_Surveying, Civil Engineering

Chap6_Sec1.ppt

Chap6_Sec1.ppt

Topic 2 area & volume

Topic 2 area & volume

Area_Contour.ppt

Area_Contour.ppt

Computation of area

Computation of area

Areas and Definite Integrals.ppt

Areas and Definite Integrals.ppt

HOME ASSIGNMENT (0).pptx

HOME ASSIGNMENT (0).pptx

HOME ASSIGNMENT omar ali.pptx

HOME ASSIGNMENT omar ali.pptx

S2 9 areas and volumes

S2 9 areas and volumes

Methods of computation of area in Surveying.ppt

Methods of computation of area in Surveying.ppt

Overviewing the techniques of Numerical Integration.pdf

Overviewing the techniques of Numerical Integration.pdf

Lecture 18 M5.pdf

Lecture 18 M5.pdf

Calculate_distance_and_bearing_between Latitude_Longitude_Points.docx

Calculate_distance_and_bearing_between Latitude_Longitude_Points.docx

Calculate_distance_and_bearing_between Latitude_Longitude_Points.docx

Calculate_distance_and_bearing_between Latitude_Longitude_Points.docx

AREA AND PERIMETER

AREA AND PERIMETER

Integration

Integration

ch6&7.pdf

ch6&7.pdf

Numerical Solution of Diffusion Equation by Finite Difference Method

Numerical Solution of Diffusion Equation by Finite Difference Method

pvpresentationfsecmodified-130908085906-.pptx

Photovoltaic (PV) systems convert sunlight directly into electricity and can power various applications where other power sources are impractical or unavailable. PV systems are increasingly popular and have many uses such as providing power for remote telecommunications towers, water pumping, lighting, and powering devices in developing areas that lack electricity infrastructure. PV power is also used for off-shore navigational aids, highway signs, recreational vehicles, and large utility-scale systems.

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Integrated Weed Management (IWM) utilizes multiple weed control techniques including blind tillage, mechanical weeders, and herbicides. Blind tillage uproots extra plants and broadleaved weeds after crop planting without damaging young crops. Mechanical weeders like dry land weeders, power rotary weeders, and tractor operated multi row rotary weeders are used to remove shallow rooted and inter row weeds in various row crops. The cono weeder is a manual weeder that efficiently removes weeds between crop rows.

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Both Thysanura and Collembola are wingless insect orders that undergo incomplete metamorphosis. They share several characteristics including being apterygote, having an absence of pleural sulcus, and indirect sperm transfer. Thysanura have long filamentous tails while Collembola have a peg-like structure called a collophore. Both orders use abdominal appendages like styli and tenacula for locomotion and escaping predators.

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Fungi have diverse body forms ranging from unicellular yeasts to multicellular mushrooms. They obtain nutrients by absorption and secrete enzymes to break down food sources. Fungi play important ecological roles as decomposers, symbionts such as mycorrhizal partners of plants, and parasites of plants and animals. They reproduce both sexually through spores and asexually through mitotic spores. Major fungal groups are classified based on sexual reproductive structures like asci or basidia. Fungi interact with humans both beneficially through roles in decomposition, food production, and medicine, and harmfully as causes of food spoilage, plant diseases, and some serious human infections.

Practical 2 Chain and Compass Surveying - Computation of areas.ppt

The document describes procedures for conducting a chain and cross staff survey to determine the area of an irregularly shaped plot of land. It involves identifying corners along the boundary and measuring offsets from the baseline using chain and cross staff. The plot is divided into triangles and trapezoids. Their individual areas are calculated using appropriate formulae and summed to get the total area. Sample problems are provided to demonstrate drawing maps based on chainage readings and calculating area using tabular methods and triangulation.

Transpiration and it's significance.pptx

This document contains a multiple choice quiz on the topic of transpiration and its significance. It includes 60 questions testing knowledge of plant anatomy features related to transpiration like stomata, guard cells, cuticle and epidermis. It also covers the factors influencing transpiration rate, mechanisms of stomatal opening and closing, and theories proposed to explain these mechanisms like the starch-sugar hypothesis and proton transport theory. The document lists the questions, answers, and team members who created the quiz.

pvpresentationfsecmodified-130908085906-.pptx

pvpresentationfsecmodified-130908085906-.pptx

integratedweedmangement-200730175200.pptx

integratedweedmangement-200730175200.pptx

silkwormrearing-220628071406-72ff0a67 (1).pdf

silkwormrearing-220628071406-72ff0a67 (1).pdf

Principal of applicated entomology presentation

Principal of applicated entomology presentation

JAYAPRADHA 2021031034 AEN.pptx

JAYAPRADHA 2021031034 AEN.pptx

GOPAL S 2021031026 AEN 201 ppt.pptx

GOPAL S 2021031026 AEN 201 ppt.pptx

landpollution-151101164910-lva1-app6892 (1).pptx

landpollution-151101164910-lva1-app6892 (1).pptx

6-Tax-Soil-Orders-I.ppt

6-Tax-Soil-Orders-I.ppt

senseorgansofinsectsandtheirstructure-180508155900.pptx

senseorgansofinsectsandtheirstructure-180508155900.pptx

5_2018_03_05!09_27_28_AM.pptx

5_2018_03_05!09_27_28_AM.pptx

Practical 2 Chain and Compass Surveying - Computation of areas.ppt

Practical 2 Chain and Compass Surveying - Computation of areas.ppt

Transpiration and it's significance.pptx

Transpiration and it's significance.pptx

Randomised Optimisation Algorithms in DAPHNE

Slides from talk:
Aleš Zamuda: Randomised Optimisation Algorithms in DAPHNE .
Austrian-Slovenian HPC Meeting 2024 – ASHPC24, Seeblickhotel Grundlsee in Austria, 10–13 June 2024
https://ashpc.eu/

Discovery of An Apparent Red, High-Velocity Type Ia Supernova at 𝐳 = 2.9 wi...

We present the JWST discovery of SN 2023adsy, a transient object located in a host galaxy JADES-GS
+
53.13485
−
27.82088
with a host spectroscopic redshift of
2.903
±
0.007
. The transient was identified in deep James Webb Space Telescope (JWST)/NIRCam imaging from the JWST Advanced Deep Extragalactic Survey (JADES) program. Photometric and spectroscopic followup with NIRCam and NIRSpec, respectively, confirm the redshift and yield UV-NIR light-curve, NIR color, and spectroscopic information all consistent with a Type Ia classification. Despite its classification as a likely SN Ia, SN 2023adsy is both fairly red (
�
(
�
−
�
)
∼
0.9
) despite a host galaxy with low-extinction and has a high Ca II velocity (
19
,
000
±
2
,
000
km/s) compared to the general population of SNe Ia. While these characteristics are consistent with some Ca-rich SNe Ia, particularly SN 2016hnk, SN 2023adsy is intrinsically brighter than the low-
�
Ca-rich population. Although such an object is too red for any low-
�
cosmological sample, we apply a fiducial standardization approach to SN 2023adsy and find that the SN 2023adsy luminosity distance measurement is in excellent agreement (
≲
1
�
) with
Λ
CDM. Therefore unlike low-
�
Ca-rich SNe Ia, SN 2023adsy is standardizable and gives no indication that SN Ia standardized luminosities change significantly with redshift. A larger sample of distant SNe Ia is required to determine if SN Ia population characteristics at high-
�
truly diverge from their low-
�
counterparts, and to confirm that standardized luminosities nevertheless remain constant with redshift.

Authoring a personal GPT for your research and practice: How we created the Q...

Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.

Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdf

Ozturkcan, S., Berndt, A., & Angelakis, A. (2024). Mending clothing to support sustainable fashion. Presented at the 31st Annual Conference by the Consortium for International Marketing Research (CIMaR), 10-13 Jun 2024, University of Gävle, Sweden.

Compexometric titration/Chelatorphy titration/chelating titration

Classification
Metal ion ion indicators
Masking and demasking reagents
Estimation of Magnisium sulphate
Calcium gluconate
Complexometric Titration/ chelatometry titration/chelating titration, introduction, Types-
1.Direct Titration
2.Back Titration
3.Replacement Titration
4.Indirect Titration
Masking agent, Demasking agents
formation of complex
comparition between masking and demasking agents,
Indicators/Metal ion indicators/ Metallochromic indicators/pM indicators,
Visual Technique,PM indicators (metallochromic), Indicators of pH, Redox Indicators
Instrumental Techniques-Photometry
Potentiometry
Miscellaneous methods.
Complex titration with EDTA.

快速办理(UAM毕业证书)马德里自治大学毕业证学位证一模一样

学校原件一模一样【微信：741003700 】《(UAM毕业证书)马德里自治大学毕业证学位证》【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
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三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才

GBSN - Biochemistry (Unit 6) Chemistry of Proteins

Chemistry of Proteins

MICROBIAL INTERACTION PPT/ MICROBIAL INTERACTION AND THEIR TYPES // PLANT MIC...

MICROBIAL INTERACTION PPT/ MICROBIAL INTERACTION AND THEIR TYPES // PLANT MIC...ABHISHEK SONI NIMT INSTITUTE OF MEDICAL AND PARAMEDCIAL SCIENCES , GOVT PG COLLEGE NOIDA

Microbial interaction
Microorganisms interacts with each other and can be physically associated with another organisms in a variety of ways.
One organism can be located on the surface of another organism as an ectobiont or located within another organism as endobiont.
Microbial interaction may be positive such as mutualism, proto-cooperation, commensalism or may be negative such as parasitism, predation or competition
Types of microbial interaction
Positive interaction: mutualism, proto-cooperation, commensalism
Negative interaction: Ammensalism (antagonism), parasitism, predation, competition
I. Mutualism:
It is defined as the relationship in which each organism in interaction gets benefits from association. It is an obligatory relationship in which mutualist and host are metabolically dependent on each other.
Mutualistic relationship is very specific where one member of association cannot be replaced by another species.
Mutualism require close physical contact between interacting organisms.
Relationship of mutualism allows organisms to exist in habitat that could not occupied by either species alone.
Mutualistic relationship between organisms allows them to act as a single organism.
Examples of mutualism:
i. Lichens:
Lichens are excellent example of mutualism.
They are the association of specific fungi and certain genus of algae. In lichen, fungal partner is called mycobiont and algal partner is called
II. Syntrophism:
It is an association in which the growth of one organism either depends on or improved by the substrate provided by another organism.
In syntrophism both organism in association gets benefits.
Compound A
Utilized by population 1
Compound B
Utilized by population 2
Compound C
utilized by both Population 1+2
Products
In this theoretical example of syntrophism, population 1 is able to utilize and metabolize compound A, forming compound B but cannot metabolize beyond compound B without co-operation of population 2. Population 2is unable to utilize compound A but it can metabolize compound B forming compound C. Then both population 1 and 2 are able to carry out metabolic reaction which leads to formation of end product that neither population could produce alone.
Examples of syntrophism:
i. Methanogenic ecosystem in sludge digester
Methane produced by methanogenic bacteria depends upon interspecies hydrogen transfer by other fermentative bacteria.
Anaerobic fermentative bacteria generate CO2 and H2 utilizing carbohydrates which is then utilized by methanogenic bacteria (Methanobacter) to produce methane.
ii. Lactobacillus arobinosus and Enterococcus faecalis:
In the minimal media, Lactobacillus arobinosus and Enterococcus faecalis are able to grow together but not alone.
The synergistic relationship between E. faecalis and L. arobinosus occurs in which E. faecalis require folic acid
23PH301 - Optics - Optical Lenses.pptx

Under graduate Physics - Optics

Sexuality - Issues, Attitude and Behaviour - Applied Social Psychology - Psyc...

A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!

Direct Seeded Rice - Climate Smart Agriculture

Direct Seeded Rice - Climate Smart AgricultureInternational Food Policy Research Institute- South Asia Office

PPT on Direct Seeded Rice presented at the three-day 'Training and Validation Workshop on Modules of Climate Smart Agriculture (CSA) Technologies in South Asia' workshop on April 22, 2024.
fermented food science of sauerkraut.pptx

This ppt contains the production of a fermented food name - sauerkraut

Describing and Interpreting an Immersive Learning Case with the Immersion Cub...

Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.

Farming systems analysis: what have we learnt?.pptx

Presentation given at the official farewell of Prof Ken Gillet at Wageningen on 13 June 2024

Immersive Learning That Works: Research Grounding and Paths Forward

We will metaverse into the essence of immersive learning, into its three dimensions and conceptual models. This approach encompasses elements from teaching methodologies to social involvement, through organizational concerns and technologies. Challenging the perception of learning as knowledge transfer, we introduce a 'Uses, Practices & Strategies' model operationalized by the 'Immersive Learning Brain' and ‘Immersion Cube’ frameworks. This approach offers a comprehensive guide through the intricacies of immersive educational experiences and spotlighting research frontiers, along the immersion dimensions of system, narrative, and agency. Our discourse extends to stakeholders beyond the academic sphere, addressing the interests of technologists, instructional designers, and policymakers. We span various contexts, from formal education to organizational transformation to the new horizon of an AI-pervasive society. This keynote aims to unite the iLRN community in a collaborative journey towards a future where immersive learning research and practice coalesce, paving the way for innovative educational research and practice landscapes.

The binding of cosmological structures by massless topological defects

Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.

Methods of grain storage Structures in India.pdf

•Post-harvestlossesaccountforabout10%oftotalfoodgrainsduetounscientificstorage,insects,rodents,micro-organismsetc.,
•Totalfoodgrainproductioninindiais311milliontonnesandstorageis145mt.InIndia,annualstoragelosseshavebeenestimated14mtworthofRs.7,000croreinwhichinsectsaloneaccountfornearlyRs.1,300crores.
•InIndiaoutofthetotalproduction,about30%ismarketablesurplus
•Remaining70%isretainedandstoredbyfarmersforconsumption,seed,feed.Hence,growerneedstoragefacilitytoholdaportionofproducetosellwhenthemarketingpriceisfavourable
•TradersandCo-operativesatmarketcentresneedstoragestructurestoholdgrainswhenthetransportfacilityisinadequate

Microbiology of Central Nervous System INFECTIONS.pdf

Microbiology of CNS infection

8.Isolation of pure cultures and preservation of cultures.pdf

Isolation of pure culture, its various method.

Randomised Optimisation Algorithms in DAPHNE

Randomised Optimisation Algorithms in DAPHNE

Discovery of An Apparent Red, High-Velocity Type Ia Supernova at 𝐳 = 2.9 wi...

Discovery of An Apparent Red, High-Velocity Type Ia Supernova at 𝐳 = 2.9 wi...

Authoring a personal GPT for your research and practice: How we created the Q...

Authoring a personal GPT for your research and practice: How we created the Q...

Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdf

Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdf

Compexometric titration/Chelatorphy titration/chelating titration

Compexometric titration/Chelatorphy titration/chelating titration

快速办理(UAM毕业证书)马德里自治大学毕业证学位证一模一样

快速办理(UAM毕业证书)马德里自治大学毕业证学位证一模一样

GBSN - Biochemistry (Unit 6) Chemistry of Proteins

GBSN - Biochemistry (Unit 6) Chemistry of Proteins

MICROBIAL INTERACTION PPT/ MICROBIAL INTERACTION AND THEIR TYPES // PLANT MIC...

MICROBIAL INTERACTION PPT/ MICROBIAL INTERACTION AND THEIR TYPES // PLANT MIC...

23PH301 - Optics - Optical Lenses.pptx

23PH301 - Optics - Optical Lenses.pptx

Sexuality - Issues, Attitude and Behaviour - Applied Social Psychology - Psyc...

Sexuality - Issues, Attitude and Behaviour - Applied Social Psychology - Psyc...

Direct Seeded Rice - Climate Smart Agriculture

Direct Seeded Rice - Climate Smart Agriculture

fermented food science of sauerkraut.pptx

fermented food science of sauerkraut.pptx

Describing and Interpreting an Immersive Learning Case with the Immersion Cub...

Describing and Interpreting an Immersive Learning Case with the Immersion Cub...

Juaristi, Jon. - El canon espanol. El legado de la cultura española a la civi...

Juaristi, Jon. - El canon espanol. El legado de la cultura española a la civi...

Farming systems analysis: what have we learnt?.pptx

Farming systems analysis: what have we learnt?.pptx

Immersive Learning That Works: Research Grounding and Paths Forward

Immersive Learning That Works: Research Grounding and Paths Forward

The binding of cosmological structures by massless topological defects

The binding of cosmological structures by massless topological defects

Methods of grain storage Structures in India.pdf

Methods of grain storage Structures in India.pdf

Microbiology of Central Nervous System INFECTIONS.pdf

Microbiology of Central Nervous System INFECTIONS.pdf

8.Isolation of pure cultures and preservation of cultures.pdf

8.Isolation of pure cultures and preservation of cultures.pdf

- 2. Introduction The computation of area is very essential to determine the catchment area of river, dam and reservoir. Its also important for planning and management of any engineering project. For initial reports and estimates, low precision methods can be used. When a high level of accuracy is required, a professional engineer or a land surveyor should be employed. The area is expressed in ft2, m2, km2, acres, hectares.
- 3. Methods to Compute Area The method of computation of area depends on the shape of the boundary of the surveyed area and accuracy required. If the plan is bounded by straight boundaries, it can be tackle by subdividing the total area into simple geometrical shapes, like triangle, rectangle, trapezoidal etc… and the area of the figure are computed from the dimensions. If the boundaries are irregular, they are replaced by short straight boundaries and the area is computed using approximate method. While if the boundaries are very irregular, the area can be determined by using planimeter.
- 4. Computation of Area The surveyed area may be calculated from plotted plan by following rules. 1. Mid ordinate rule 2. Average ordinate rule 3. Trapezoidal rule 4. Simpson’s one third rule
- 5. Mid Ordinate Rule The method is used with the assumption that the boundaries between the edge of the ordinates are straight lines. The base line is divided into a number of divisions and the ordinates are measured at the mid points of each division.
- 6. The area is calculated from following formula, Area = ∆ = Common distance x Sum of mid ordinates = (h1 x d) + (h2 x d) + …… + (hn x d) = d (h1+ h2+….. +hn) Where, n = Number of divisions d = common distance between ordinates h1, h2, … hn = Mid ordinates
- 7. Average Ordinate Rule This rule also assume that the boundaries between the edges of the ordinates are straight lines. The offsets are measured to each of the points of the divisions of the base line. The area is given by following equation, Area = ∆ = average ordinate x Length of the base
- 8. Trapezoidal Rule This rule is based on the assumption that the figures are trapezoids. The rule is more accurate than the previous two rules which are approximate versions of the trapezoidal rule.
- 9. The area of the first trapezoid is given by Similarly, the area of the second trapezoid is given by So, the total area isgivenby ∆ = ∆1 + ∆2 + …. ∆n Total area = (O1 + 2O2 + 2O3 + 2O4 +… + 2On-1 + On) x (d/2) = (O1 + On + 2(O2 + O3 + O4 +…+ On-1)) x (d/2) = (Common distance/2) x [(1st ordinate +last ordinate) + 2(sum of other ordinates)]
- 10. Simpson’s One Third Rule This rule assumes that the short lengths of boundary between the ordinates are parabolic arcs. So this rule is some times called the parabolic rule. This method is more useful when the boundary line departs considerably from straight line.
- 11. Here, O1, O2, O3 = Three consecutiveordinates d = Common distance between the ordinates Now, Area of AF2DC = Area of AFDC + Area of segment F2DEf Area of trapezium = Area of segment =
- 12. So, the area between the first two divisions, Similarly, the area between next two divisions, Total area = (Common distance/3) x [(1st ordinate + last ordinate) + 4(sum of even ordinates) + 2(sum of odd ordinates)]
- 13. Computation of Volume The volume of earth work is calculated by following two method after calculation of cross sectional area, 1. Trapezoidal rule 2. Prismoidal rule
- 14. Trapezoidal rule Volume, V= (d/2) x [A1+An+ 2(A2+A3+…..+An-1)] = (Common distance/2) x [(1st section area + last section area) + 2(sum of area of other section)] d
- 15. Prismoidal rule Volume, V = (d/3) x [A1+An+ 4(A2+A4+…..+An-1) + 2 (A3+A5+…..+An-2)] Limitation: The prismoidal formula is applicable when there are odd number of sections. If the number of sections are even, the section is treated separately and area is calculated according to the trapezoidal rule.
- 16. Thank You Stay tuned with us Like, Share & Subscribe