Question

The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. Height of the bucket is 30 cm. How many liters of water it can hold ?

(1 litre = 1000 cm³ )

Answer 1

Radius of one circular end, r₁ = 14 cm

Radius of other circular end, r₂ = 7 cm

Height of the bucket, h = 30 cm

∴ Volume of water in the bucket = Volume of frustum of cone
$$\begin{gathered} =\frac{1}{3}\mathrm{\pi }h\left(r_1^2+r_1{r}_2+r_2^2\right) \\ =\frac{1}{3}\times \frac{22}{7}\times 30\times \left({14}^2+14\times 7+7^2\right) \\ =\frac{1}{3}\times \frac{22}{7}\times 30\times 343 \\ =10780{\mathrm{cm}}^3 \end{gathered}$$
$$\begin{gathered} =\frac{10780}{1000} \\ =10.780\mathrm{L} \end{gathered}$$
Thus, the bucket can hold 10.780 litres of water.