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8.7 Sphere

The simplest example of a sphere is a ball. One can call here that a circle is a set of points in a plane that are equidistant from one point in the plane. If this is extended to the third dimension, we have all points in space equidistant from one particular point forming a sphere.

The sphere has only one surfaces and its surface area = 4p r2

The volume of a sphere =

Example 1

If the lateral area of a right circular cylinder is 24p and its radius is 2 . What is its height.

Solution :

Lateral area of a right circular cylinder = 2 p r h

Since r = 2 , LA = 4 p h.

Given that LA = 24 p

\ 24 p = 4 p h

\ h = 6 units

Example 2

Find the total area of the right circular cylinder with a radius of 10 units and a height of 5 units.

Solution :

Total area of a right circular cylinder is 2prh + 2p r2

If r = 10 and h = 5

Total area = 100p + 200 p = 300 p

Example 3

What is the radius of the right circular cylinder with volume 18p cubic units and height = 2.

Solution :

Volume of right circular cylinder = pr2h

where r = radius and h = height

Given that V = 18p and h = 2

\ 18p = pr2 ´ 2

or r2 = 9

r = 3 units

Example 4

If the perimeter and slant height of a regular pyramid are 10 and 3 respectively. Find its lateral area.

Solution :

For a regular pyramid lateral area, LA =´ p ´ l

where p = perimeter and l = slant height

Given that p = 10 and l = 3

\ LA = ´ 10 ´ 3 = 15 square units.

Example 5

If the volume of a sphere is 36p. Find its radius and surface area.

Solution :


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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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