Question

A bucket is in the form of a frustum of a cone. Its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm, respectively. Find how many litres of water can the bucket hold.

Answer 1

Greater diameter of the frustum = 56 cm
Greater radius of the frustum = R = 28 cm
Smaller diameter of the frustum = 42 cm
Radius of the smaller end of the frustum = r = 21 cm
Height of the frustum = h = 15 cm

Capacity of the frustum
$$\begin{gathered} =\frac{1}{3}\mathrm{\pi }h\left(R^2+r^2+Rr\right) \\ =\frac{1}{3}\times \frac{22}{7}\times 15\left({28}^2+{21}^2+28\times 21\right) \\ =\frac{22\times 5}{7}\times 1813 \\ =28490{\mathrm{cm}}^3=28.49\mathrm{litres} \end{gathered}$$