### Solved Examples

**Question 1: **Find the volume of the cylinder with a radius of 5 cm and height 8 cm

** Solution: **

Given radius = 5 cm

Height = 8 cm

Volume of a cylinder is $\pi$ r$^{2}$ h

V = 3.14 $\times$ 25 $\times$ 8

= 628

Therefore, volume of the cylinder for the given data is 628 cm$^{3}$.

**Question 2: **David has a rectangular garden pond 5 m long and 3 m wide. How many litres of water does he need to fill it to a depth of 45 cm.

** Solution: **

Dimensions of rectangular garden pond = 5 m x 3 m x 45 cm

Convert all the given units in centimeters.

Dimensions = 5 m x 3 m x 45 cm = 500 cm x 300 cm x 45 cm

Now volume of cuboid = 500 $\times$ 300 $\times$ 45

= 6750000 cm$^{3}$

As 1 litre = 1000 cm$^{3}$,

$\frac{6750000}{1000}$ = 6750

Therefore, David will need 6750 litres of water to fill rectangular pond to a depth of 45 cm.

**Question 3: **Find the volume of a sphere of radius 24 m.

** Solution: **

Given Radius = 24m

Formula for volume of sphere is given by

$\frac{4}{3}$ $\pi$ r$^{3}$

= $\frac{4}{3}$ $\times$ 3.14 $\times$ (24)$^{3}$

= 57876.48

Therefore, the volume of the sphere is 57876.48 m$^{3}$

**Question 4: **Find the volume of a pyramid with square base of side 8 cm and a height of 12 cm.

** Solution: **

Height = 12 cm

Area of base = Side$^{2}$ (l$^2$) = 8$^{2}$ = 64

The formula for volume of pyramid is $\frac{1}{3}$ * l$^{2}$ $\times$ h

= $\frac{1}{3}$ $\times$ 64 $\times$ 12

= 256

Therefore, the volume of the pyramid for the given data is 256 cm$^{3}$.

**Question 5: **Find the volume of a cone of radius 8 cm and height 13 cm?

** Solution: **

Given Radius = 8 cm

Height = 13 cm

The formula for volume of cone is $\frac{1}{3}$ $\times$ $\pi$ r$^{2}$ $\times$ h

= 870.83

Therefore, the volume of a cone is 870.83 cm$^{3}$

**Question 6: **Find the volume of a triangular pyramid of apothem length 9 cm, base length 12 cm and height 15 cm ?

** Solution: **

Given,

a = 9 cm

b = 12 cm

h = 15 cm

Volume of a triangular pyramid

= $\frac{1}{6}$ abh

= $\frac{1}{6}$ * 9 * 12 * 15

= 270

Therefore, the volume of a triangular pyramid is 270cm$^{3}$.

**Question 7: **Find the volume of a pentagonal pyramid of apothem length 7 cm, base length 8 cm and height 10 cm ?

** Solution: **

Given,

a = 7 cm

b = 8 cm

h = 10 cm

Volume of a pentagonal pyramid

= $\frac{5}{6}$ abh

= 466.67

Therefore, the volume of a pentagonal pyramid for the given data is 466.67 cm$^{3}$