Question

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

Answer 1

Radius of the circular top of washing tub, r₁ = 20 cm

Radius of the circular bottom of washing tub, r₂ = 15 cm

Height of the washing tub, h = 21 cm

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

$$\begin{gathered} =\frac{1}{3}\mathrm{\pi }h\left(r_1^2+r_1{r}_2+r_2^2\right) \\ =\frac{1}{3}\times \frac{22}{7}\times 21\times \left({20}^2+20\times 15+{15}^2\right) \\ =22\times \left(400+300+225\right) \\ =22\times 925 \\ =20350{\mathrm{cm}}^3 \end{gathered}$$
$$\begin{gathered} =\frac{20350}{1000}\mathrm{L}\left(1\mathrm{L}=1000{\mathrm{cm}}^3\right) \\ =20.35\mathrm{L} \end{gathered}$$
Thus, the capacity of the tub is 20.35 litres.