#### Question

A washing tub in the shape of a frustum of a cone has a height of 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub? ( \[\pi = \frac{22}{7}\]).

#### Solution

Radius of the circular top of washing tub, r_{1} = 20 cm

Radius of the circular bottom of washing tub, r_{2} = 15 cm

Height of the washing tub, h = 21 cm

∴ Capacity of the washing tub = Volume of frustum of cone

\[= \frac{1}{3}\pi h\left( r_1^2 + r_1 r_2 + r_2^2 \right)\]

\[ = \frac{1}{3} \times \frac{22}{7} \times 21 \times \left( {20}^2 + 20 \times 15 + {15}^2 \right)\]

\[ = 22 \times \left( 400 + 300 + 225 \right)\]

\[ = 22 \times 925\]

\[ = 20350 {cm}^3\]

\[= \frac{20350}{1000} L \left( 1 L = 1000 {cm}^3 \right)\]

\[ = 20 . 35 L\]

Thus, the capacity of the tub is 20.35 litres.