Question

If the radii of the ends of a 42-cm-high bucket are 16 cm and 11 cm, determine its capacity.

Answer 1

The bucket is shaped like a frustum.
Let the larger radius be R = 16 cm
Smaller radius = r = 11 cm
Height = h = 42 cm

Therefore capacity of the bucket can be expressed as:

$$\begin{gathered} \frac{1}{3}\mathrm{\pi }h\left(R^2+r^2+Rr\right)=\frac{1}{3}\times \frac{22}{7}\times 42\left({16}^2+{11}^2+16\times 11\right) \\ =44\left(256+121+176\right) \\ =44\times 553=24332{\mathrm{cm}}^3 \end{gathered}$$