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CHAPTER 8 : SURFACE AREA AND VOLUME

8.1 Introduction to Solid Geometry

All the geometric shapes discussed in this book till now i.e. polygons, circles etc. are planar shapes. They are called two dimensional shapes i.e. generally speaking they have only length and breadth. In the real world however every object has length breadth and height. Therefore they are called three dimensional objects. No single plane can contain such objects in totality.

Consider the simplest example of a three dimensional shape - a brick.


Figure 8.1

Shown in Figure 8.1 is a brick with length 10 cm, breadth 5 cm and height 4 cm. There cannot be a single plane which can contain the brick.

A brick has six surfaces and eight vertices. Each surface has an area which can be calculated. The sum of the areas of all the six surfaces is called the surface area of the brick.

Apart from surface area a brick has another measurable property. i.e. the space it occupies. This space occupied by the brick is called its volume. Every three dimensional (3-D) object occupies a finite volume. The 3 -D objects or geometric solids dealt within this chapter are

(1) Prism
(2) Cube
(3) Right circular cylinder
(4) Pyramid
(5) Right circular cones and
(6) Sphere

Apart from defining these objects, methods to calculate their surface area and volume are also incorporated in this chapter.

Index

8.1 Introduction to solid geometry
8.2 Prism
8.3 The cuboid and the cube
8.4 Cylinders
8.5 Pyramids
8.6 Right circular cone
8.7 Sphere

Chapter 9

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