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Mathematics for Engineers
book

Mathematics for Engineers

by Ritu Shrivastava, Ramakant Bhardwaj, Satyendra Narayan
June 2025
Intermediate to advanced
576 pages
11h 26m
English
Wiley-Scrivener
Content preview from Mathematics for Engineers

4Three-Dimensional Geometry

A diagrammatic representation of three-dimensional (3D) geometric figures. It covers the descriptions of 3D shapes, explains their nets, and defines surface area and volume. Additionally, it includes problem-solving related to the volume and surface areas of these shapes.

Objectives: This chapter

  • Describes three-dimensional (3D) geometric figures.
  • Explains the nets of three-dimensional figures.
  • Defines the surface area and volume of three-dimensional shapes.
  • Solve different levels of problems related to volume and surface areas of 3D shapes.

4.1 Introduction

Geometry is the branch of mathematics that measures two-dimensional and three-dimensional shapes or figures. The previous topic of Chapter 3 was two-dimensional shapes; here, we will learn rules and methods to measure the volume and surface of any three-directional shape.

The only difference between 2-dimensional and three-dimensional shapes is the third dimension which is Depth/height along with length and width. Any two-dimensional shape has length and width, whereas a three-dimensional solid shape also has depth, length, and breadth.

4.2 Nets of Three-Dimensional Shapes

Observe the below figure. If you look at it carefully, you can identify that this shape can make a three-dimensional shape called a cylinder. It is also known as a net of three-dimensional shape. (As an activity, draw this shape on a piece of paper and cut by its edges, try folding it to make a three-dimensional shape).

A diagram depicts the net of a cylinder, which consists of two circles representing the top and bottom faces, along with a rectangular shape that forms its curved surface. This illustration helps visualize how the three-dimensional shape can be represented in two dimensions.

This net of the cylinder has two circles (top and bottom and a rectangle ...

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Publisher Resources

ISBN: 9781394214587