12.1 Volume of Prisms and Cylinders
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* Classify three-dimensional figures according to their properties * Calculate the volumes of prisms and cylinders
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5.13.4 Volume
This document defines various 3D shapes and their volume formulas. It discusses how to calculate the volume of prisms, cylinders, pyramids, and cones. For prisms and cylinders, the volume is the area of the base multiplied by the height, regardless of whether the shape is right or oblique. The volume of a pyramid is one-third the area of the base multiplied by the height. For a cone, the volume is one-third pi times the area of the base times the height. Several examples are provided to demonstrate calculating volumes of different 3D shapes using the appropriate formulas.
5.13.3 Volume
The document discusses calculating the volumes of various geometric shapes like prisms, cylinders, pyramids, and cones. It provides formulas for calculating volumes of right and oblique prisms and cylinders as well as pyramids and cones. Examples are given applying the volume formulas to specific shapes with given measurements.
5.13.3 Volume
The document discusses calculating volumes of geometric solids such as prisms, cylinders, pyramids, and cones. It provides formulas for calculating volumes of right and oblique prisms and cylinders as well as formulas for pyramids and cones. Examples are given of applying the volume formulas to various solids. The key points are that volumes of prisms and cylinders do not depend on whether they are right or oblique and the formulas for calculating volumes are V = Bh for prisms and cylinders, V = 1/3Bh for pyramids, and V = 1/3πr^2h for cones.
12.1 Volume of Prisms and Cylinders
The document discusses classifying and calculating volumes of prisms and cylinders. It defines key terms like face, edge, and vertex. Prisms have two parallel congruent polygon bases connected by faces that are parallelograms, while cylinders have two parallel congruent circular bases. The volume of any prism or cylinder can be calculated as V=Bh, where B is the area of the base and h is the height or altitude. Examples calculate the volumes of different prisms and cylinders.
Obj. 44 Volume
The student can calculate the volumes of prisms, cylinders, pyramids, and cones. The document defines different types of prisms and their components. It explains that the volume formula for any prism or cylinder is the base area multiplied by the height or altitude, regardless of whether it is right or oblique. Formulas are provided for calculating the volumes of pyramids and cones. Several examples are worked through applying the volume formulas to different shapes.
Obj. 51 Prisms and Cylinders
This document provides information about calculating the surface area and volume of prisms and cylinders. It defines right and oblique prisms, and explains that the volume formula is the same for both as V=Bh, where B is the base area and h is the altitude or height. The same is true for cylinders, where the volume is V=πr^2h. Examples are given to find the volume of various prisms and cylinders. Formulas are also provided for calculating the lateral and total surface area of prisms as S=L+2B, where L is the lateral area calculated as L=Ph, and B is the base area. For cylinders, the lateral area formula is L=C*h,
12.1 solid geometry
The document discusses concepts in solid geometry including:
- Classifying three-dimensional figures according to their properties such as polyhedra, prisms, pyramids, cylinders, and cones.
- Relating two-dimensional nets to their three-dimensional shapes.
- Analyzing cross-sections of three-dimensional shapes.
- Key terms such as faces, edges, vertices, altitude, Platonic solids, Euler's formula, and surface area are defined.
- Examples of describing three-dimensional shapes from their nets and calculating surface areas of prisms are provided.
002 s.a. of prisms
This document discusses how to find the lateral area and surface area of a polyhedron called a prism. It defines key terms like polyhedron, altitude, lateral area, and net. It then explains that the lateral area of a right prism can be found using the formula LA = Hp, where H is the height and p is the perimeter of the base. The surface area of a right prism can be found using the formula SA = LA + 2B, where LA is the lateral area and B is the area of one base. Examples are provided to demonstrate calculating the lateral area and surface area of a right prism with a regular hexagonal base.
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5.13.4 Volume
This document defines various 3D shapes and their volume formulas. It discusses how to calculate the volume of prisms, cylinders, pyramids, and cones. For prisms and cylinders, the volume is the area of the base multiplied by the height, regardless of whether the shape is right or oblique. The volume of a pyramid is one-third the area of the base multiplied by the height. For a cone, the volume is one-third pi times the area of the base times the height. Several examples are provided to demonstrate calculating volumes of different 3D shapes using the appropriate formulas.
5.13.3 Volume
The document discusses calculating the volumes of various geometric shapes like prisms, cylinders, pyramids, and cones. It provides formulas for calculating volumes of right and oblique prisms and cylinders as well as pyramids and cones. Examples are given applying the volume formulas to specific shapes with given measurements.
5.13.3 Volume
The document discusses calculating volumes of geometric solids such as prisms, cylinders, pyramids, and cones. It provides formulas for calculating volumes of right and oblique prisms and cylinders as well as formulas for pyramids and cones. Examples are given of applying the volume formulas to various solids. The key points are that volumes of prisms and cylinders do not depend on whether they are right or oblique and the formulas for calculating volumes are V = Bh for prisms and cylinders, V = 1/3Bh for pyramids, and V = 1/3πr^2h for cones.
12.1 Volume of Prisms and Cylinders
The document discusses classifying and calculating volumes of prisms and cylinders. It defines key terms like face, edge, and vertex. Prisms have two parallel congruent polygon bases connected by faces that are parallelograms, while cylinders have two parallel congruent circular bases. The volume of any prism or cylinder can be calculated as V=Bh, where B is the area of the base and h is the height or altitude. Examples calculate the volumes of different prisms and cylinders.
Obj. 44 Volume
The student can calculate the volumes of prisms, cylinders, pyramids, and cones. The document defines different types of prisms and their components. It explains that the volume formula for any prism or cylinder is the base area multiplied by the height or altitude, regardless of whether it is right or oblique. Formulas are provided for calculating the volumes of pyramids and cones. Several examples are worked through applying the volume formulas to different shapes.
Obj. 51 Prisms and Cylinders
This document provides information about calculating the surface area and volume of prisms and cylinders. It defines right and oblique prisms, and explains that the volume formula is the same for both as V=Bh, where B is the base area and h is the altitude or height. The same is true for cylinders, where the volume is V=πr^2h. Examples are given to find the volume of various prisms and cylinders. Formulas are also provided for calculating the lateral and total surface area of prisms as S=L+2B, where L is the lateral area calculated as L=Ph, and B is the base area. For cylinders, the lateral area formula is L=C*h,
12.1 solid geometry
The document discusses concepts in solid geometry including:
- Classifying three-dimensional figures according to their properties such as polyhedra, prisms, pyramids, cylinders, and cones.
- Relating two-dimensional nets to their three-dimensional shapes.
- Analyzing cross-sections of three-dimensional shapes.
- Key terms such as faces, edges, vertices, altitude, Platonic solids, Euler's formula, and surface area are defined.
- Examples of describing three-dimensional shapes from their nets and calculating surface areas of prisms are provided.
002 s.a. of prisms
This document discusses how to find the lateral area and surface area of a polyhedron called a prism. It defines key terms like polyhedron, altitude, lateral area, and net. It then explains that the lateral area of a right prism can be found using the formula LA = Hp, where H is the height and p is the perimeter of the base. The surface area of a right prism can be found using the formula SA = LA + 2B, where LA is the lateral area and B is the area of one base. Examples are provided to demonstrate calculating the lateral area and surface area of a right prism with a regular hexagonal base.
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Solid geometry involves classifying and analyzing three-dimensional shapes. Key concepts include polyhedra composed of polygons, prisms with two parallel congruent bases, pyramids with a polygonal base meeting at a common vertex, and using nets which can be folded to form three-dimensional shapes. Formulas relate the number of vertices, edges and faces of polyhedra. Surface area calculations involve finding the total area of each face.
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The document discusses different types of three-dimensional shapes studied in solid geometry. It provides definitions and examples of cubes, rectangular prisms, cylinders, spheres, cones, and pyramids. It also gives the formulas for calculating the volume and surface area of these shapes. For each shape, it provides examples of applying the formulas to solve volume and surface area problems.
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Classify three-dimensional figures according to their properties.
Use nets and cross sections to analyze three-dimensional figures.
Extend midpoint and distance formulas to three dimensions
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Three-Dimensional Geometry discusses spatial relations and three-dimensional figures. It explains that three-dimensional figures have faces, edges, and vertices. The document provides examples and formulas for calculating the volumes of prisms, cylinders, cones, pyramids and cubes. It also discusses surface area and provides examples and formulas for calculating surface areas of prisms and cylinders.
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A MENSURATIO PPT WHICH GIVES EXACT KNOWLEDGE MUST SEE IT
IF YOU WANT ME TO MAKE YOUR OWN SUBJECT PPT CALL ME ON NUMBER
9968821561
Geom12point2and3 97
The document summarizes different types of geometric solids and how to calculate their surface areas. It discusses prisms, cylinders, pyramids, cones, and spheres. For each solid, it defines key terms like base, height, lateral face, radius, and provides the surface area formulas. Examples are included to demonstrate calculating the surface area of different solids.
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PPT CONSISTS OF
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CONES , CYLINDER,CIRCLE ,RECTANGLE,SQUARE
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Chapter 10 day 1 s.a. of prisms
1. The document discusses geometric concepts related to polyhedrons including prisms. It defines key terms like polyhedron, lateral area, surface area, altitude, net, prism, right prism, and provides formulas to calculate lateral area and surface area of right prisms.
2. Examples are given to identify 3D shapes from their nets and to draw orthographic views of objects. The document also contains classwork on drawing nets and calculating measurements of prisms.
3. Geometric concepts like polyhedrons, prisms, lateral area, surface area, and orthographic views are defined and formulas/examples are provided for calculating measurements and drawing representations of prisms.
Chapter 10 day 1 s.a. of prisms
1. The document discusses geometric concepts related to polyhedrons including prisms. It defines key terms like polyhedron, lateral area, surface area, altitude, net, prism, right prism, and provides formulas to calculate lateral area and surface area of right prisms.
2. Examples are given to identify 3D shapes from their nets and to draw orthographic views of objects. The document also contains classwork on drawing nets and calculating measurements of prisms.
3. Geometric concepts like polyhedrons, prisms, lateral area, surface area, and orthographic views are defined and formulas/examples are provided for calculating measurements and drawing representations of 3D objects.
Chapter 10 day 1 s.a. of prisms
1. The document discusses geometric concepts related to polyhedrons including prisms. It defines key terms like polyhedron, lateral area, surface area, altitude, net, prism, right prism, and provides examples of calculating lateral area and surface area of right prisms.
2. Examples are given of identifying 3D shapes from their nets and drawing orthographic views of objects. Formulas are provided for finding the lateral area and surface area of right prisms given the height and parameters of the base.
3. The document is a lesson on geometric concepts involving polyhedrons, prisms, nets, lateral area, surface area, and includes examples and practice problems for students.
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Polygons can be regular or irregular. Regular polygons have all sides and angles equal, while irregular polygons do not. Common polygons include triangles, quadrilaterals, pentagons, and hexagons. Polygons are 2D shapes with straight sides. 3D shapes include polyhedra with flat faces that are polygons, as well as non-polyhedral shapes like cylinders, cones, and spheres. Polyhedra include the five Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron) as well as prisms and pyramids. Prisms have two identical polygon bases and parallelogram sides, while pyramids have one polygon base and triangular sides
Geometry of shapes
This document defines and explains properties of various quadrilaterals:
- Parallelograms have two pairs of parallel sides and opposite sides are congruent and angles are congruent. The diagonals of a parallelogram bisect each other.
- Rectangles are parallelograms with four right angles. Squares are rectangles with four congruent sides.
- Rhombuses are parallelograms with four congruent sides. The diagonals of a rhombus are perpendicular.
- Trapezoids have one pair of parallel sides called bases. The median of a trapezoid is parallel to its bases and is half the sum of the bases.
Visualizing solid shapes
A polyhedron is a three-dimensional solid shape bounded by flat polygons. It has faces, edges, and vertices. Faces are the flat polygons that make up the sides of the polyhedron. Edges are the lines where faces meet. Vertices are the points where edges intersect. Regular polyhedra have identical regular polygons for faces and the same number of faces meeting at each vertex. Prisms and pyramids are examples of polyhedra. Euler's formula relates the number of faces, edges and vertices of any polyhedron as F + V = E + 2.
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This document discusses the volume computation of different solid figures including prisms, pyramids, cones, cylinders, and spheres. It provides examples of calculating the volume of each type of solid figure. For prisms, the volume is calculated as V=Bh, where B is the area of the base and h is the height. For pyramids and cones, the volume is calculated as V=1/3Bh. For spheres, the volume is calculated as V=4/3πr^3, where r is the radius of the sphere.
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12.2 Prisms and Cylinders
This document discusses calculating the surface area and volume of prisms and cylinders. It provides formulas for calculating the lateral surface area, total surface area, and volume of both prisms and cylinders. For prisms, the lateral area is calculated as L=Ph, where P is the perimeter and h is the height. The total surface area of a prism is the lateral area plus twice the area of the base. For cylinders, the lateral area is calculated as L=Ch, where C is the circumference and h is the height. The total surface area of a cylinder is the lateral area plus twice the area of the circular base. The volume of both prisms and cylinders is calculated as V=Bh, where B is the
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Solid geometry involves classifying and analyzing three-dimensional shapes. Key concepts include polyhedra composed of polygons, prisms with two parallel congruent bases, pyramids with a polygonal base meeting at a common vertex, and using nets which can be folded to form three-dimensional shapes. Formulas relate the number of vertices, edges and faces of polyhedra. Surface area calculations involve finding the total area of each face.
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The chapter Lifelines of National Economy in Class 10 Geography focuses on the various modes of transportation and communication that play a vital role in the economic development of a country. These lifelines are crucial for the movement of goods, services, and people, thereby connecting different regions and promoting economic activities.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
BBR 2024 Summer Sessions Interview Training
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Healing can occur in two ways: Regeneration and Repair
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Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
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Social Laboratory, New Zealand,
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Lifelines of National Economy chapter for Class 10 STUDY MATERIAL PDF
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12.1 Volume of Prisms and Cylinders
- 1. Prisms and Cylinders The student is able to (I can): • Classify three-dimensional figures according to their properties • Calculate the volumes of prisms and cylinders
- 2. face – the flat polygonal surface on a three-dimensional figure. edge – the segment that is the intersection of two faces. vertex – the point that is the intersection of three or more edges. face edge vertex •
- 3. polyhedron – a three-dimensional figure composed of polygons. (plural polyhedra) prism – two parallel congruent polygon bases connected by faces that are parallelograms. cylinder – two parallel congruent circular bases and a curved surface that connects the bases.
- 4. pyramid – a polygonal base with triangular faces that meet at a common vertex. cone – a circular base and a curved surface that connects the base to a vertex.
- 5. right prism – a prism whose faces are all rectangles. (Assume a prism is a right prism unless noted otherwise.) oblique prism – a prism whose faces are not rectangles. altitude – a perpendicular segment joining the planes of the bases (the height).
- 6. Volume Let’s consider a deck of cards. If a deck is stacked neatly, it resembles a right rectangular prism. The volume of the prism is V = Bh, where B is the area of one card, and h is the height of the deck. If we shift the deck so that it becomes an oblique prism, does it have the same number of cards?
- 7. For any prism, whether right or oblique, the volume is V = Bh where h is the altitude, not the length of the lateral edge.
- 8. Likewise, for cylinders, it doesn’t matter whether the cylinder is right or oblique, the volume is V = Bh = r2h
- 9. Examples Find the volume of each figure: 1. 2. 10 ft. 8 ft. 3 m 19 m
- 10. Examples Find the volume of each figure: 1. 2. 10 ft. 8 ft. 3 m 19 m ( ) 2 2 3 9 m = = B 3 (9 )(19) 171 m V = = ( )( ) 2 5 10 172.05 180 4tan 5 = = B V = (172.05)(8) = 1376.4 ft3