NCERT Class 9 Mathematics

SURFACE AREAS AND VOLUMES 235

Since a hemisphere is half of a sphere, can you guess what the volume of a

hemisphere will be? Yes, it is^3

14

of

23

r =^2

3 ✁r

(^3).
So, Volume of a Hemisphere =^3

2

3

r

where r is the radius of the hemisphere.

Let us take some examples to illustrate the use of these formulae.

Example 17 : Find the volume of a sphere of radius 11.2 cm.

Solution :Required volume =

4

3 ✁r

3

=

422

11.2 11.2 11.2

37

✂ ✂ ✂ ✂ cm^3 = 5887.32 cm^3

Example 18 : A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the
metal is 7.8 g per cm^3 , find the mass of the shot-putt.

Solution : Since the shot-putt is a solid sphere made of metal and its mass is equal to
the product of its volume and density, we need to find the volume of the sphere.

Now, volume of the sphere =^3

4

3

✄r

=

(^422) 4.9 4.9 4.9 cm 3
37

☎ ☎ ☎ ☎

= 493 cm^3 (nearly)

Further, mass of 1 cm^3 of metal is 7.8 g.

Therefore, mass of the shot-putt = 7.8 × 493 g

= 3845.44 g = 3.85 kg (nearly)

Example 19 : A hemispherical bowl has a radius of 3.5 cm. What would be the
volume of water it would contain?

Solution : The volume of water the bowl can contain

=^3

2

3

✄r

=

222

3.5 3.5 3.5

37

✂ ✂ ✂ ✂ cm^3 = 89.8 cm^3