1. The document discusses sections of solids and development of surfaces of solids. It provides definitions and illustrations of sectioning a solid using section planes, and developing the surface of a solid.
2. Methods of developing surfaces are described for prisms, cylinders, cones, pyramids, and other shapes. Common engineering applications of development include sheet metal works.
3. Several example problems are provided to illustrate finding sectional views, true shapes of sections, and developing the surfaces of remaining solids for various objects cut by different section planes.
6. Section of solids and development of surfaces.pptAmitSolankiSVNIT
This document provides information about sections of solids, development, and intersections in engineering drawing. It discusses how to section a solid using an imaginary cutting plane and the different types of section planes. Typical section planes and their resulting shapes are shown for different solids. Development is defined as unfolding the hollowed-out sheet of a solid to show its unfolded shape. Several examples of developments are provided for solids like prisms, cylinders, cones, pyramids, and frustums. The document also contains several problems demonstrating how to draw projections, sectional views, true shapes of sections, and developments for various solids that are cut by different section planes.
1. The document provides instructions for sectioning solids, developing surfaces of solids, and intersections of solids. It includes definitions of terms like section plane and sectioning.
2. Illustrations show how to determine the true shape of sections and develop the surfaces of remaining parts of solids that have been cut by a section plane.
3. The document contains examples of typical section planes and resulting shapes for various solids like cones, pyramids, and prisms. It also provides practice problems for using these techniques.
The document discusses the development of surfaces of solids. It begins by defining development as the shape of an unfolded sheet obtained by cutting open a hollow object from one side. Developments are 2D representations that show the true area and dimensions of an object. Various solids like prisms, cylinders, cones, pyramids and their sections can be developed. Developments have many engineering applications in sheet metal fabrication. The document then provides examples of developing different solids and solving problems involving finding the developments of cut sections. It concludes by constructing the path of a particle moving in a helical path around a cone.
1. A cone with a 50mm base diameter and 70mm axis is cut by a section plane inclined at 45 degrees to the horizontal plane through the base end of an end generator.
2. The projections, sectional views, true shape of the section, and development of the remaining solid are drawn.
3. Key features included the section plane cutting the cone, projections showing the cut portion, and the true shape and development unfolding the remaining surface.
1. The document contains contact information for Pranav Kulshrestha and sections from a technical document on projections of solids, including sections of solids, developments, and intersections with examples and illustrations.
2. It provides definitions and examples of sectioning a solid with different section planes, as well as typical section planes and resulting shapes.
3. Developments of surfaces are defined as unfolding the hollow object into a 2D sheet, and examples of developments are given for different solids.
1. The document discusses different types of solids and their classification into two groups - Group A includes solids with bases of the same shape as the top, like cylinders and prisms. Group B includes solids with the base of one shape and just a point as the top, like cones and pyramids.
2. It then provides dimensional parameters and definitions for different solids like triangular faces, slant edges, generators, etc. It also discusses positions of solids relative to planes like standing, resting, and lying.
3. The rest of the document contains 10 problems solving different configurations of solids through their projections using standard procedures like making visible lines dark and hidden lines dotted. This includes
The document discusses various types of solids and their classification. It provides information on dimensional parameters of solids like prisms, pyramids, cylinders and cones. It also describes positions of solids like standing, resting and lying on horizontal and vertical planes. Several example problems are given with step-by-step solutions to draw projections of different solids in various orientations.
This document contains information about various 3D shapes or solids. It divides solids into two groups: Group A includes cylinders and prisms which have bases and tops of the same shape, while Group B includes cones and pyramids which have a pointed top. The document provides details on the dimensional parameters, projections and solving problems related to different solids. It also discusses positions of the center of gravity for freely suspended solids.
6. Section of solids and development of surfaces.pptAmitSolankiSVNIT
This document provides information about sections of solids, development, and intersections in engineering drawing. It discusses how to section a solid using an imaginary cutting plane and the different types of section planes. Typical section planes and their resulting shapes are shown for different solids. Development is defined as unfolding the hollowed-out sheet of a solid to show its unfolded shape. Several examples of developments are provided for solids like prisms, cylinders, cones, pyramids, and frustums. The document also contains several problems demonstrating how to draw projections, sectional views, true shapes of sections, and developments for various solids that are cut by different section planes.
1. The document provides instructions for sectioning solids, developing surfaces of solids, and intersections of solids. It includes definitions of terms like section plane and sectioning.
2. Illustrations show how to determine the true shape of sections and develop the surfaces of remaining parts of solids that have been cut by a section plane.
3. The document contains examples of typical section planes and resulting shapes for various solids like cones, pyramids, and prisms. It also provides practice problems for using these techniques.
The document discusses the development of surfaces of solids. It begins by defining development as the shape of an unfolded sheet obtained by cutting open a hollow object from one side. Developments are 2D representations that show the true area and dimensions of an object. Various solids like prisms, cylinders, cones, pyramids and their sections can be developed. Developments have many engineering applications in sheet metal fabrication. The document then provides examples of developing different solids and solving problems involving finding the developments of cut sections. It concludes by constructing the path of a particle moving in a helical path around a cone.
1. A cone with a 50mm base diameter and 70mm axis is cut by a section plane inclined at 45 degrees to the horizontal plane through the base end of an end generator.
2. The projections, sectional views, true shape of the section, and development of the remaining solid are drawn.
3. Key features included the section plane cutting the cone, projections showing the cut portion, and the true shape and development unfolding the remaining surface.
1. The document contains contact information for Pranav Kulshrestha and sections from a technical document on projections of solids, including sections of solids, developments, and intersections with examples and illustrations.
2. It provides definitions and examples of sectioning a solid with different section planes, as well as typical section planes and resulting shapes.
3. Developments of surfaces are defined as unfolding the hollow object into a 2D sheet, and examples of developments are given for different solids.
1. The document discusses different types of solids and their classification into two groups - Group A includes solids with bases of the same shape as the top, like cylinders and prisms. Group B includes solids with the base of one shape and just a point as the top, like cones and pyramids.
2. It then provides dimensional parameters and definitions for different solids like triangular faces, slant edges, generators, etc. It also discusses positions of solids relative to planes like standing, resting, and lying.
3. The rest of the document contains 10 problems solving different configurations of solids through their projections using standard procedures like making visible lines dark and hidden lines dotted. This includes
The document discusses various types of solids and their classification. It provides information on dimensional parameters of solids like prisms, pyramids, cylinders and cones. It also describes positions of solids like standing, resting and lying on horizontal and vertical planes. Several example problems are given with step-by-step solutions to draw projections of different solids in various orientations.
This document contains information about various 3D shapes or solids. It divides solids into two groups: Group A includes cylinders and prisms which have bases and tops of the same shape, while Group B includes cones and pyramids which have a pointed top. The document provides details on the dimensional parameters, projections and solving problems related to different solids. It also discusses positions of the center of gravity for freely suspended solids.
This document discusses sections and developments of solids. It begins by defining sectioning a solid as cutting it with an imaginary cutting plane to understand its internal details. Two common section planes are described. Developments of solids are defined as unfolding the hollow object to show its unfolded sheet shape. Engineering applications of developments in sheet metal industries are provided. The document then discusses important terms in sectioning and provides illustrations. It explains developments of different solids and includes nine problems demonstrating sections and developments of prisms, cones, and frustums with step-by-step solutions.
Projection of solidsProjection of solidsProjection of solidsARUNPRAKASHS7
1. The document discusses different types of solids and their classification into two groups - Group A solids having top and base of same shape, and Group B solids having base of some shape and just a point as a top.
2. It provides steps to solve problems involving solids, which involves assuming the solid standing on the plane it is inclined to, drawing the front and top views, and then considering additional inclinations to draw the final views.
3. Sample problems are given involving solids like cubes, pyramids, cylinders and cones in different orientations to the planes. Dimensional parameters, positions of solids, and techniques to determine hidden and visible lines are also described.
The document discusses sections and developments of solids. It defines sectioning a solid as cutting it with an imaginary cutting plane to understand its internal details. The cutting plane is called the section plane. It provides examples of typical section planes and resulting shapes for different solids. Developments are defined as unfolding the hollow sheet metal version of a solid completely, resulting in its unfolded 2D shape. Developments are useful for manufacturing complex objects. The document includes illustrations and examples of sectioning various solids like prisms, cylinders, cones, pyramids and finding their true shapes and developments.
1. The document describes various solids and their dimensional parameters including rectangular prisms, triangular prisms, square pyramids, cylinders, and cones. It discusses their faces, edges, and other geometric features.
2. Methods for solving problems involving solids are presented. Problems can be solved in three steps: 1) assume the solid is standing on the plane it is inclined to, 2) draw projections considering the solid's inclination, and 3) draw final projections considering any remaining inclinations.
3. Several example problems are shown applying this three-step method to solids inclined to horizontal and vertical planes in different positions like standing, resting, or freely suspended. This includes determining front, top/
1. The document describes various solids and their classification into two groups - Group A consisting of solids with bases and tops of the same shape, and Group B consisting of solids with bases of some shape and just a point as the top.
2. Dimensional parameters of different solids like cylinders, cones, prisms and pyramids are defined. Positions of solids relative to planes are also described.
3. Three step methods for solving problems involving solids inclined to horizontal and vertical planes are outlined. Various categories of illustrated problems involving different cases are listed.
1. The document discusses different types of solids and their classification into two groups based on the shape of their top and base.
2. It provides instructions on how to solve problems involving solids by assuming their position and orientation, and drawing their front, top, and side views in three steps.
3. Examples of problems involving solids like cubes, pyramids, cylinders, and cones in different orientations are presented along with their step-by-step solutions.
1. The document discusses different types of solids and their classification into two groups: Group A solids have the same shape for the top and base, while Group B solids have the base of some shape and just a point for the top.
2. It provides details on the dimensional parameters of solids like cylinders, cones, prisms and pyramids. It also describes how to solve problems involving solids in three steps: assuming the solid standing on a reference plane, drawing the front and top views, and considering any remaining inclinations.
3. An example problem is given involving drawing the projections of a freely suspended pentagonal pyramid with conditions specified.
1. The document discusses different types of solids and their classification into two groups based on the shape of their top and base.
2. It provides instructions on how to solve problems involving solids through a three step process of assuming the solid in different positions and drawing their front and top views.
3. Examples of problems involving solids like cubes, pyramids, cylinders and cones in different orientations are presented along with their step-by-step solutions.
1. The document discusses different types of solids and their classification into two groups: Group A includes solids with bases of the same shape as the top like cylinders and prisms, while Group B includes solids with the top being a single point called the apex, like cones and pyramids.
2. It provides details on the dimensional parameters of different solids like their faces, edges, bases, etc. It also discusses different positions of solids relative to planes like standing, resting, or lying.
3. Steps to solve problems involving solids inclined to horizontal and vertical planes are outlined. The document contains examples of problems involving solids like cylinders, cones, cubes, and tetrahed
This document provides information about orthographic projections of points and lines. It begins by defining common notations used, such as labeling different views in projections. It then discusses the placement of points and lines in different quadrants and how this affects their front, top, and side views. Various examples are given of projecting points and lines that are inclined at different angles to the horizontal and vertical planes. The document also discusses determining true lengths and angles from apparent views. Traces of lines, where they intersect the planes, are defined. In all, it presents the key concepts and problem-solving process for orthographic projections of basic geometric elements.
Development of surfaces of solids -ENGINEERING DRAWING - RGPV,BHOPALAbhishek Kandare
Development of surfaces of solids
THIS SLIDE CONTAINS WHOLE SYLLABUS OF ENGINEERING DRAWING/GRAPHICS. IT IS THE MOST SIMPLE AND INTERACTIVE WAY TO LEARN ENGINEERING DRAWING.SYLLABUS IS RELATED TO rajiv gandhi proudyogiki vishwavidyalaya / rajiv gandhi TECHNICAL UNIVERSITY ,BHOPAL.
The document discusses sections and developments of solids. It defines sectioning a solid as cutting it with an imaginary cutting plane to understand its internal details. The cutting plane is called the section plane. It shows how to draw the true shape of a section and the development of the remaining solid. It provides examples of typical section planes and shapes formed for different solids. It also defines development as the shape of an unfolded sheet representing the lateral surfaces of a hollow solid. Examples of its engineering applications are given. The document concludes with problems demonstrating how to draw sections, true shapes and developments of various solids.
This document provides information on orthographic projections and the projection of points and lines. It begins by outlining important notations used in orthographic projections. It then discusses the projection of points located in different quadrants and the simple cases of projecting lines, including vertical lines, lines parallel to planes, and inclined lines. The document also covers projections where the true length, views, or inclinations are known or unknown. It defines important parameters and diagrams the relationships between true length, views, and angles. Finally, it discusses problems involving the traces of lines on planes.
This document provides information on orthographic projections including:
1. Notations used for different views of points and lines in orthographic projections. Front, top, and side views are denoted with primes.
2. Key concepts like quadrants, true length, line inclinations, and traces (points where a line intersects the planes) are explained.
3. Examples are given of projecting points and lines in different positions in relation to the planes. Projections are shown of lines that are vertical, parallel, or inclined to the planes.
4. Ten important parameters are defined for describing lines, including true length, view angles, lengths of front and top views, and positions of ends. Graphical
The document discusses different types of solids and their projections. It classifies solids into two groups - Group A solids have the same shape for the top and base, including cylinders and prisms. Group B solids have the base of some shape and a point for the top, including cones and pyramids. It provides steps for drawing projections of solids in different positions and orientations, including problems showing projections of specific solids like pyramids, cylinders, and cones in various configurations.
The document discusses different types of solids and their projections. It is divided into two major sections.
Section one classifies solids into two groups - Group A solids have the same shape for the top and base, such as prisms and cylinders. Group B solids have the base of one shape and a point top called the apex, such as pyramids and cones. It then provides examples and diagrams of different solids.
Section two provides steps for solving problems involving solids. It explains how to assume the solid is standing on a plane based on its orientation, and how to draw front and top views. It also categorizes example problems and provides solutions for problems involving solids like py
1. The document classifies solids into two groups - Group A solids have bases and tops of the same shape, while Group B solids have a base of some shape and just a point as a top.
2. Problems involving solids are solved in three steps: 1) assume the solid is standing on its base plane, 2) consider the solid's inclination, 3) consider any remaining inclination to draw the final views.
3. Key solids discussed include cylinders, cones, prisms, pyramids, tetrahedrons, and their dimensional parameters, positions of centers of gravity, and examples of how to draw their projections when resting, inclined, or freely suspended.
1) The document classifies solids into two groups - Group A solids have bases and tops of the same shape, while Group B solids have a base of some shape and just a point as a top.
2) Problems involving solids are solved in three steps - assuming the solid standing on a reference plane, drawing projections based on that, then considering additional inclinations.
3) Freely suspended solids have their center of gravity located at specific points along their axis depending on the solid type - cylinders and prisms have their CG at the midpoint, while cones and pyramids have their CG a quarter of the way from the base.
This document discusses sections and developments of solids. It begins by defining sectioning a solid as cutting it with an imaginary cutting plane to understand its internal details. Two common section planes are described. Developments of solids are defined as unfolding the hollow object to show its unfolded sheet shape. Engineering applications of developments in sheet metal industries are provided. The document then discusses important terms in sectioning and provides illustrations. It explains developments of different solids and includes nine problems demonstrating sections and developments of prisms, cones, and frustums with step-by-step solutions.
Projection of solidsProjection of solidsProjection of solidsARUNPRAKASHS7
1. The document discusses different types of solids and their classification into two groups - Group A solids having top and base of same shape, and Group B solids having base of some shape and just a point as a top.
2. It provides steps to solve problems involving solids, which involves assuming the solid standing on the plane it is inclined to, drawing the front and top views, and then considering additional inclinations to draw the final views.
3. Sample problems are given involving solids like cubes, pyramids, cylinders and cones in different orientations to the planes. Dimensional parameters, positions of solids, and techniques to determine hidden and visible lines are also described.
The document discusses sections and developments of solids. It defines sectioning a solid as cutting it with an imaginary cutting plane to understand its internal details. The cutting plane is called the section plane. It provides examples of typical section planes and resulting shapes for different solids. Developments are defined as unfolding the hollow sheet metal version of a solid completely, resulting in its unfolded 2D shape. Developments are useful for manufacturing complex objects. The document includes illustrations and examples of sectioning various solids like prisms, cylinders, cones, pyramids and finding their true shapes and developments.
1. The document describes various solids and their dimensional parameters including rectangular prisms, triangular prisms, square pyramids, cylinders, and cones. It discusses their faces, edges, and other geometric features.
2. Methods for solving problems involving solids are presented. Problems can be solved in three steps: 1) assume the solid is standing on the plane it is inclined to, 2) draw projections considering the solid's inclination, and 3) draw final projections considering any remaining inclinations.
3. Several example problems are shown applying this three-step method to solids inclined to horizontal and vertical planes in different positions like standing, resting, or freely suspended. This includes determining front, top/
1. The document describes various solids and their classification into two groups - Group A consisting of solids with bases and tops of the same shape, and Group B consisting of solids with bases of some shape and just a point as the top.
2. Dimensional parameters of different solids like cylinders, cones, prisms and pyramids are defined. Positions of solids relative to planes are also described.
3. Three step methods for solving problems involving solids inclined to horizontal and vertical planes are outlined. Various categories of illustrated problems involving different cases are listed.
1. The document discusses different types of solids and their classification into two groups based on the shape of their top and base.
2. It provides instructions on how to solve problems involving solids by assuming their position and orientation, and drawing their front, top, and side views in three steps.
3. Examples of problems involving solids like cubes, pyramids, cylinders, and cones in different orientations are presented along with their step-by-step solutions.
1. The document discusses different types of solids and their classification into two groups: Group A solids have the same shape for the top and base, while Group B solids have the base of some shape and just a point for the top.
2. It provides details on the dimensional parameters of solids like cylinders, cones, prisms and pyramids. It also describes how to solve problems involving solids in three steps: assuming the solid standing on a reference plane, drawing the front and top views, and considering any remaining inclinations.
3. An example problem is given involving drawing the projections of a freely suspended pentagonal pyramid with conditions specified.
1. The document discusses different types of solids and their classification into two groups based on the shape of their top and base.
2. It provides instructions on how to solve problems involving solids through a three step process of assuming the solid in different positions and drawing their front and top views.
3. Examples of problems involving solids like cubes, pyramids, cylinders and cones in different orientations are presented along with their step-by-step solutions.
1. The document discusses different types of solids and their classification into two groups: Group A includes solids with bases of the same shape as the top like cylinders and prisms, while Group B includes solids with the top being a single point called the apex, like cones and pyramids.
2. It provides details on the dimensional parameters of different solids like their faces, edges, bases, etc. It also discusses different positions of solids relative to planes like standing, resting, or lying.
3. Steps to solve problems involving solids inclined to horizontal and vertical planes are outlined. The document contains examples of problems involving solids like cylinders, cones, cubes, and tetrahed
This document provides information about orthographic projections of points and lines. It begins by defining common notations used, such as labeling different views in projections. It then discusses the placement of points and lines in different quadrants and how this affects their front, top, and side views. Various examples are given of projecting points and lines that are inclined at different angles to the horizontal and vertical planes. The document also discusses determining true lengths and angles from apparent views. Traces of lines, where they intersect the planes, are defined. In all, it presents the key concepts and problem-solving process for orthographic projections of basic geometric elements.
Development of surfaces of solids -ENGINEERING DRAWING - RGPV,BHOPALAbhishek Kandare
Development of surfaces of solids
THIS SLIDE CONTAINS WHOLE SYLLABUS OF ENGINEERING DRAWING/GRAPHICS. IT IS THE MOST SIMPLE AND INTERACTIVE WAY TO LEARN ENGINEERING DRAWING.SYLLABUS IS RELATED TO rajiv gandhi proudyogiki vishwavidyalaya / rajiv gandhi TECHNICAL UNIVERSITY ,BHOPAL.
The document discusses sections and developments of solids. It defines sectioning a solid as cutting it with an imaginary cutting plane to understand its internal details. The cutting plane is called the section plane. It shows how to draw the true shape of a section and the development of the remaining solid. It provides examples of typical section planes and shapes formed for different solids. It also defines development as the shape of an unfolded sheet representing the lateral surfaces of a hollow solid. Examples of its engineering applications are given. The document concludes with problems demonstrating how to draw sections, true shapes and developments of various solids.
This document provides information on orthographic projections and the projection of points and lines. It begins by outlining important notations used in orthographic projections. It then discusses the projection of points located in different quadrants and the simple cases of projecting lines, including vertical lines, lines parallel to planes, and inclined lines. The document also covers projections where the true length, views, or inclinations are known or unknown. It defines important parameters and diagrams the relationships between true length, views, and angles. Finally, it discusses problems involving the traces of lines on planes.
This document provides information on orthographic projections including:
1. Notations used for different views of points and lines in orthographic projections. Front, top, and side views are denoted with primes.
2. Key concepts like quadrants, true length, line inclinations, and traces (points where a line intersects the planes) are explained.
3. Examples are given of projecting points and lines in different positions in relation to the planes. Projections are shown of lines that are vertical, parallel, or inclined to the planes.
4. Ten important parameters are defined for describing lines, including true length, view angles, lengths of front and top views, and positions of ends. Graphical
The document discusses different types of solids and their projections. It classifies solids into two groups - Group A solids have the same shape for the top and base, including cylinders and prisms. Group B solids have the base of some shape and a point for the top, including cones and pyramids. It provides steps for drawing projections of solids in different positions and orientations, including problems showing projections of specific solids like pyramids, cylinders, and cones in various configurations.
The document discusses different types of solids and their projections. It is divided into two major sections.
Section one classifies solids into two groups - Group A solids have the same shape for the top and base, such as prisms and cylinders. Group B solids have the base of one shape and a point top called the apex, such as pyramids and cones. It then provides examples and diagrams of different solids.
Section two provides steps for solving problems involving solids. It explains how to assume the solid is standing on a plane based on its orientation, and how to draw front and top views. It also categorizes example problems and provides solutions for problems involving solids like py
1. The document classifies solids into two groups - Group A solids have bases and tops of the same shape, while Group B solids have a base of some shape and just a point as a top.
2. Problems involving solids are solved in three steps: 1) assume the solid is standing on its base plane, 2) consider the solid's inclination, 3) consider any remaining inclination to draw the final views.
3. Key solids discussed include cylinders, cones, prisms, pyramids, tetrahedrons, and their dimensional parameters, positions of centers of gravity, and examples of how to draw their projections when resting, inclined, or freely suspended.
1) The document classifies solids into two groups - Group A solids have bases and tops of the same shape, while Group B solids have a base of some shape and just a point as a top.
2) Problems involving solids are solved in three steps - assuming the solid standing on a reference plane, drawing projections based on that, then considering additional inclinations.
3) Freely suspended solids have their center of gravity located at specific points along their axis depending on the solid type - cylinders and prisms have their CG at the midpoint, while cones and pyramids have their CG a quarter of the way from the base.
Similar to Development-of-surfaces-of-solids.ppt (20)
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
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ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
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.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
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, UPRAHUL
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
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help of Advanced technologies like Remote Sensing and Geographic Information Systems is
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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.
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Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
1. 1. SECTIONS OF SOLIDS.
2. DEVELOPMENT.
3. INTERSECTIONS.
ENGINEERING APPLICATIONS
OF
THE PRINCIPLES
OF
PROJECTIONS OF SOLIDES.
STUDY CAREFULLY
THE ILLUSTRATIONS GIVEN ON
NEXT SIX PAGES !
2. SECTIONING A SOLID.
An object ( here a solid ) is cut by
some imaginary cutting plane
to understand internal details of that object.
The action of cutting is called
SECTIONING a solid
&
The plane of cutting is called
SECTION PLANE.
Two cutting actions means section planes are recommended.
A) Section Plane perpendicular to Vp and inclined to Hp.
( This is a definition of an Aux. Inclined Plane i.e. A.I.P.)
NOTE:- This section plane appears
as a straight line in FV.
B) Section Plane perpendicular to Hp and inclined to Vp.
( This is a definition of an Aux. Vertical Plane i.e. A.V.P.)
NOTE:- This section plane appears
as a straight line in TV.
Remember:-
1. After launching a section plane
either in FV or TV, the part towards observer
is assumed to be removed.
2. As far as possible the smaller part is
assumed to be removed.
OBSERVER
ASSUME
UPPER PART
REMOVED
OBSERVER
ASSUME
LOWER PART
REMOVED
(A)
(B)
3. ILLUSTRATION SHOWING
IMPORTANT TERMS
IN SECTIONING.
x y
TRUE SHAPE
Of SECTION
SECTION
PLANE
SECTION LINES
(450 to XY)
Apparent Shape
of section
SECTIONAL T.V.
For TV
4. Section Plane
Through Apex
Section Plane
Through Generators
Section Plane Parallel
to end generator.
Section Plane
Parallel to Axis.
Triangle Ellipse
Hyperbola
Ellipse
Cylinder through
generators.
Sq. Pyramid through
all slant edges
Trapezium
Typical Section Planes
&
Typical Shapes
Of
Sections.
5. DEVELOPMENT OF SURFACES OF SOLIDS.
MEANING:-
ASSUME OBJECT HOLLOW AND MADE-UP OF THIN SHEET. CUT OPEN IT FROM ONE SIDE AND
UNFOLD THE SHEET COMPLETELY. THEN THE SHAPE OF THAT UNFOLDED SHEET IS CALLED
DEVELOPMENT OF LATERLAL SUEFACES OF THAT OBJECT OR SOLID.
LATERLAL SURFACE IS THE SURFACE EXCLUDING SOLID’S TOP & BASE.
ENGINEERING APLICATION:
THERE ARE SO MANY PRODUCTS OR OBJECTS WHICH ARE DIFFICULT TO MANUFACTURE BY
CONVENTIONAL MANUFACTURING PROCESSES, BECAUSE OF THEIR SHAPES AND SIZES.
THOSE ARE FABRICATED IN SHEET METAL INDUSTRY BY USING
DEVELOPMENT TECHNIQUE. THERE IS A VAST RANGE OF SUCH OBJECTS.
EXAMPLES:-
Boiler Shells & chimneys, Pressure Vessels, Shovels, Trays, Boxes & Cartons, Feeding Hoppers,
Large Pipe sections, Body & Parts of automotives, Ships, Aeroplanes and many more.
WHAT IS
OUR OBJECTIVE
IN THIS TOPIC ?
To learn methods of development of surfaces of
different solids, their sections and frustums.
1. Development is different drawing than PROJECTIONS.
2. It is a shape showing AREA, means it’s a 2-D plain drawing.
3. Hence all dimensions of it must be TRUE dimensions.
4. As it is representing shape of an un-folded sheet, no edges can remain hidden
And hence DOTTED LINES are never shown on development.
But before going ahead,
note following
Important points.
Study illustrations given on next page carefully.
6. D
H
D
S
S
H
= R
L
3600
R=Base circle radius.
L=Slant height.
L= Slant edge.
S = Edge of base
H= Height S = Edge of base
H= Height D= base diameter
Development of lateral surfaces of different solids.
(Lateral surface is the surface excluding top & base)
Prisms: No.of Rectangles
Cylinder: A Rectangle
Cone: (Sector of circle) Pyramids: (No.of triangles)
Tetrahedron: Four Equilateral Triangles
All sides
equal in length
Cube: Six Squares.
7.
= R
L
3600
R= Base circle radius of cone
L= Slant height of cone
L1 = Slant height of cut part.
Base side
Top side
L= Slant edge of pyramid
L1 = Slant edge of cut part.
DEVELOPMENT OF
FRUSTUM OF CONE
DEVELOPMENT OF
FRUSTUM OF SQUARE PYRAMID
STUDY NEXT NINE PROBLEMS OF
SECTIONS & DEVELOPMENT
FRUSTUMS
8. X Y
X1
Y1
A
B
C
E
D
a
e
d
b
c
A B C D E A
DEVELOPMENT
a”
b”
c”
d”
e”
Problem 1: A pentagonal prism , 30 mm base side & 50 mm axis
is standing on Hp on it’s base with one side of the base perpendicular to VP.
It is cut by a section plane inclined at 45º to the HP, through mid point of axis.
Draw Fv, sec.Tv & sec. Side view. Also draw true shape of section and
Development of surface of remaining solid.
Solution Steps:for sectional views:
Draw three views of standing prism.
Locate sec.plane in Fv as described.
Project points where edges are getting
Cut on Tv & Sv as shown in illustration.
Join those points in sequence and show
Section lines in it.
Make remaining part of solid dark.
For True Shape:
Draw x1y1 // to sec. plane
Draw projectors on it from
cut points.
Mark distances of points
of Sectioned part from Tv,
on above projectors from
x1y1 and join in sequence.
Draw section lines in it.
It is required true shape.
For Development:
Draw development of entire solid. Name from
cut-open edge I.e. A. in sequence as shown.
Mark the cut points on respective edges.
Join them in sequence in st. lines.
Make existing parts dev.dark.
9. Y
h
a
b
c
d
e
g
f
X a’ b’ d’ e’
c’ g’ f’
h’
o’
X1
Y1
g” h”f” a”e” b”d” c”
A
B
C
D
E
F
A
G
H
SECTIONAL T.V
SECTIONAL S.V
DEVELOPMENT
Problem 2: A cone, 50 mm base diameter and 70 mm axis is
standing on it’s base on Hp. It cut by a section plane 450 inclined
to Hp through base end of end generator.Draw projections,
sectional views, true shape of section and development of surfaces
of remaining solid.
Solution Steps:for sectional views:
Draw three views of standing cone.
Locate sec.plane in Fv as described.
Project points where generators are
getting Cut on Tv & Sv as shown in
illustration.Join those points in
sequence and show Section lines in it.
Make remaining part of solid dark.
For True Shape:
Draw x1y1 // to sec. plane
Draw projectors on it from
cut points.
Mark distances of points
of Sectioned part from Tv,
on above projectors from
x1y1 and join in sequence.
Draw section lines in it.
It is required true shape.
For Development:
Draw development of entire solid.
Name from cut-open edge i.e. A.
in sequence as shown.Mark the cut
points on respective edges.
Join them in sequence in curvature.
Make existing parts dev.dark.
10. X Y
e’
a’ b’ d’
c’ g’ f’
h’
o’
o’
Problem 3: A cone 40mm diameter and 50 mm axis is resting on one generator on Hp( lying on Hp)
which is // to Vp.. Draw it’s projections.It is cut by a horizontal section plane through it’s base
center. Draw sectional TV, development of the surface of the remaining part of cone.
A
B
C
D
E
F
A
G
H
O
a1
h1
g1
f1
e1
d1
c1
b1
o1
SECTIONAL T.V
DEVELOPMENT
(SHOWING TRUE SHAPE OF SECTION)
HORIZONTAL
SECTION PLANE
h
a
b
c
d
e
g
f
O
Follow similar solution steps for Sec.views - True shape – Development as per previous problem!
11. A.V.P300 inclined to Vp
Through mid-point of axis.
X Y
1
2
3 4
5
6
7
8
b’ f’
a’ e’
c’ d’
a
b
c
d
e
f
a1
d1
b1
e1
c1
f1
X1
Y1
AS SECTION PLANE IS IN T.V.,
CUT OPEN FROM BOUNDRY EDGE C1 FOR DEVELOPMENT.
C D E F A B C
DEVELOPMENT
SECTIONAL F.V.
Problem 4: A hexagonal prism. 30 mm base side &
55 mm axis is lying on Hp on it’s rect.face with axis
// to Vp. It is cut by a section plane normal to Hp and
300 inclined to Vp bisecting axis.
Draw sec. Views, true shape & development.
Use similar steps for sec.views & true shape.
NOTE: for development, always cut open object from
From an edge in the boundary of the view in which
sec.plane appears as a line.
Here it is Tv and in boundary, there is c1 edge.Hence
it is opened from c and named C,D,E,F,A,B,C.
Note the steps to locate
Points 1, 2 , 5, 6 in sec.Fv:
Those are transferred to
1st TV, then to 1st Fv and
Then on 2nd Fv.
12. 1’
2’
3’
4’
5’
6’
7’
7
1
5
4
3
2
6
7
1
6
5
4
3
2
a
b
c
d
e
f
g
4
4 5
3
6
2
7
1
A
B
C
D
E
A
F
G
O
O’
d’e’ c’f’ g’b’ a’
X Y
X1
Y1
F.V.
SECTIONAL
TOP VIEW.
Problem 5:A solid composed of a half-cone and half- hexagonal pyramid is
shown in figure.It is cut by a section plane 450 inclined to Hp, passing through
mid-point of axis.Draw F.v., sectional T.v.,true shape of section and
development of remaining part of the solid.
( take radius of cone and each side of hexagon 30mm long and axis 70mm.)
Note:
Fv & TV 8f two solids
sandwiched
Section lines style in both:
Development of
half cone & half pyramid:
13. o’
h
a
b
c
d
g
f
o e
a’ b’ c’ g’ d’f’ e’
h’
X Y
= R
L
3600
R=Base circle radius.
L=Slant height.
A
B
C
D
E
F
G
H
A
O
1
3
2
4
7
6
5
L
1
2
3
4
5
6
7
1’
2’
3’ 4’
5’
6’
7’
Problem 6: Draw a semicircle 0f 100 mm diameter and inscribe in it a largest
circle.If the semicircle is development of a cone and inscribed circle is some
curve on it, then draw the projections of cone showing that curve.
Solution Steps:
Draw semicircle of given diameter, divide it in 8 Parts and inscribe in it
a largest circle as shown.Name intersecting points 1, 2, 3 etc.
Semicircle being dev.of a cone it’s radius is slant height of cone.( L )
Then using above formula find R of base of cone. Using this data
draw Fv & Tv of cone and form 8 generators and name.
Take o -1 distance from dev.,mark on TL i.e.o’a’ on Fv & bring on o’b’
and name 1’ Similarly locate all points on Fv. Then project all on Tv
on respective generators and join by smooth curve.
TO DRAW PRINCIPAL
VIEWS FROM GIVEN
DEVELOPMENT.
14. o’
h
a
b
c
d
g
f
o e
a’ b’ c’ g’ d’f’ e’
h’
X Y
= R
L
3600
R=Base circle radius.
L=Slant height.
A
B
C
D
E
F
G
H
A
O
1
3
2
4
7
6
5
L
1
2
3
4
5
6
7
1’
2’
3’ 4’
5’
6’
7’
Problem 6: Draw a semicircle 0f 100 mm diameter and inscribe in it a largest
circle.If the semicircle is development of a cone and inscribed circle is some
curve on it, then draw the projections of cone showing that curve.
Solution Steps:
Draw semicircle of given diameter, divide it in 8 Parts and inscribe in it
a largest circle as shown.Name intersecting points 1, 2, 3 etc.
Semicircle being dev.of a cone it’s radius is slant height of cone.( L )
Then using above formula find R of base of cone. Using this data
draw Fv & Tv of cone and form 8 generators and name.
Take o -1 distance from dev.,mark on TL i.e.o’a’ on Fv & bring on o’b’
and name 1’ Similarly locate all points on Fv. Then project all on Tv
on respective generators and join by smooth curve.
TO DRAW PRINCIPAL
VIEWS FROM GIVEN
DEVELOPMENT.
15.
16. h
a
b
c
d
g
f
e
o’
a’ b’ d’
c’ g’ f’
h’ e’
X Y
A
B
C
D
E
F
G
H
A
O L
= R
L
3600
R=Base circle radius.
L=Slant height.
1’
2’ 3’
4’
5’
6’
7’
1
2
3
4
5
6
7
Problem 7:Draw a semicircle 0f 100 mm diameter and inscribe in it a largest
rhombus.If the semicircle is development of a cone and rhombus is some curve
on it, then draw the projections of cone showing that curve.
TO DRAW PRINCIPAL
VIEWS FROM GIVEN
DEVELOPMENT.
Solution Steps:
Similar to previous
Problem:
17. a’ b’ c’ d’
o’
e’
a
b
c
d
o e
X Y
A
B
C
D
E
A
O
2
3
4
1
Problem 8: A half cone of 50 mm base diameter, 70 mm axis, is standing on it’s half base on HP with it’s flat face
parallel and nearer to VP.An inextensible string is wound round it’s surface from one point of base circle and
brought back to the same point.If the string is of shortest length, find it and show it on the projections of the cone.
1 2
3
4
1’
2’ 3’ 4’
TO DRAW A CURVE ON
PRINCIPAL VIEWS
FROM DEVELOPMENT. Concept: A string wound
from a point up to the same
Point, of shortest length
Must appear st. line on it’s
Development.
Solution steps:
Hence draw development,
Name it as usual and join
A to A This is shortest
Length of that string.
Further steps are as usual.
On dev. Name the points of
Intersections of this line with
Different generators.Bring
Those on Fv & Tv and join
by smooth curves.
Draw 4’ a’ part of string dotted
As it is on back side of cone.
18. X Y
e’
a’ b’ d’
c’ g’ f’
h’
o’
h
a
b
c
d
e
g
f
O
DEVELOPMENT
A
B
C
D
E
F
A
G
H
O
1
2
3
4
6 5
7
1’
2’
3’
4’
5’
6’
7’
1
2
3
4
5
6
7
HELIX CURVE
Problem 9: A particle which is initially on base circle of a cone, standing
on Hp, moves upwards and reaches apex in one complete turn around the cone.
Draw it’s path on projections of cone as well as on it’s development.
Take base circle diameter 50 mm and axis 70 mm long.
It’s a construction of curve
Helix of one turn on cone:
Draw Fv & Tv & dev.as usual
On all form generators & name.
Construction of curve Helix::
Show 8 generators on both views
Divide axis also in same parts.
Draw horizontal lines from those
points on both end generators.
1’ is a point where first horizontal
Line & gen. b’o’ intersect.
2’ is a point where second horiz.
Line & gen. c’o’ intersect.
In this way locate all points on Fv.
Project all on Tv.Join in curvature.
For Development:
Then taking each points true
Distance From resp.generator
from apex, Mark on development
& join.
19. X Y
1
2
3
4
5
6
7
8
9
10
11
12
Q 15.26: draw the projections of a cone resting on the ground on its base and show on them, the shortest path
by which a point P, starting from a point on the circumference of the base and moving around the cone will
return to the same point. Base ofn cone 65 mm diameter ; axis 75 mm long.
1
2
12
3
11
4
10
5
9
6
8 7
2
3
4
5
6
7
8
9
10
11
12
1
θ=141º
20. Q 15.26: A right circular cone base 30 mm side and height 50 mm rests on its base on H.P. It is cut by a
section plane perpendicular to the V.P., inclined at 45º to the H.P. and bisecting the axis. Draw the projections
of the truncated cone and develop its lateral surface.
X Y
1
2
3
4
5
6
7
8
9
10
11
12
1
2
12
3
11
4
10
5
9
6
8 7
2
3
4
5
6
7
8
9
10
11
12
1
a
b
c
k
d
e
f
g
h
i
l
j
a
f
b
c
k
d
e
g
h
i
l
j
A
C
D
E
B
A
F
G
H
I
J
K
L
θ=103º
21. Q 14.11: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all
the edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the
VP, inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side
view and true shape of the section. Also draw its development.
X
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
11
41
21 31
Y
A
B
C
D
A
O
1
1
2
3
4
22. Q 14.14: A pentagonal pyramid , base 30mm side and axis 60 mm long is lying on one of its triangular faces
on the HP with the axis parallel to the VP. A vertical section plane, whose HT bisects the top view of the axis
and makes an angle of 30º with the reference line, cuts the pyramid removing its top part. Draw the top view,
sectional front view and true shape of the section and development of the surface of the remaining portion of
the pyramid.
Y
X
a’ b’ e’ c’ d’
a
b
c
d
e
o
o’
60
c’d’ o’
a’
b’e’
30
a1
b1
c1
d1
e1
o1
1’
2’
3’
4’
5’
6’
1
2
3
4
5
6
31’
41’
21’
11’
61’
51’
O
A
B
C
D
E
A
1
2
3
4
5
6
1
5
6
23. Q 14.11: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP with
two edges of the base perpendicular to the VP. It is cut by a section plane, perpendicular to the
VP, inclined at 45º to the HP and bisecting the axis. Draw its sectional top view and true shape of
the section. Also draw its development.
X
o’
Y
A
B
C
D
A
O
a b
c
d
o
a’ d’ b’ c’
1
2
3
4
1’ 4’
2’ 3’
2
3
1
2
True length
of slant
edge
1 4
1
1
4
2 3
2
3
True length
of slant
edge
24. Q.15.11: A right circular cylinder, base 50 mm diameter and axis 60 mm long, is standing on HP on its
base. It has a square hole of size 25 in it. The axis of the hole bisects the axis of the cylinder and is
perpendicular to the VP. The faces of the square hole are equally inclined with the HP. Draw its
projections and develop lateral surface of the cylinder.
Y
1
2
3
4
5
6
7
8
9
10
11
12
X
1’
2’
12’
3’
11’
4’
10’
5’
9’
6’
8’ 7’
a’
b’
c’
d’
1 2 3 4 5 6 7 8 9 10 11 12 1
a
a
b
d
b
d
c
c
A
B
D
C C
B
D
A
a c
25. Q.15.21: A frustum of square pyramid has its base 50 mm side, top 25 mm side and axis 75 mm. Draw
the development of its lateral surface. Also draw the projections of the frustum (when its axis is vertical
and a side of its base is parallel to the VP), showing the line joining the mid point of a top edge of one
face with the mid point of the bottom edge of the opposite face, by the shortest distance.
Y
X
50 25
75
a b
c
d
a1 b1
c1
d1
a’
d’
b’
c’
a1’
d1’
b1’
c1’
o
o’
True
length of
slant
edge
A1
B1
C1
D1
A1
A
B
C
D
A
P
Q
R
S
p’
p
q’
q
r’
r
s’
s
26. Q: A square prism of 40 mm edge of the base and 65 mm height stands on its base on the HP with
vertical faces inclined at 45º with the VP. A horizontal hole of 40 mm diameter is drilled centrally
through the prism such that the hole passes through the opposite vertical edges of the prism, draw
the development og the surfaces of the prism.
Y
X
a
b
c
d
a’ b’d’ c’
a’ b’d’ c’
1’
2’
3’
4’
5’
6’
7’
8’
9’
10’
11’
12’
1
1
2
12
2
12
3
11
3
11
4 10
4 10
5
9
5
9
4
8
4
8
1 2
12
3
11
4
10
A
B
C
7
7
5
9
6
8
7 6
8
5
9
4
10
7 1
2
12
3
11 A
1
2
12
11
3
10
4
9
5
8
6
7 1
2
12
11 9
5
8
7
3
4
6
10
D