Question

The diameters of two circular ends of a bucket are 44 cm and 24 cm, and the height of the bucket is 35 cm. The capacity of the bucket is
(a) 31.7 litres
(b) 32.7 litres
(c) 33.7 litres
(d) 34.7 litres

Answer 1

(b) 32.7 litres
Let R and r be the radii of the top and base of the bucket, respectively, and let h be its height.

Then, $R=\frac{44}{2}\text{cm}=22\text{cm},r=\frac{24}{2}\text{cm}=12\text{cm},h=35\text{cm}$

Capacity of the bucket = Volume of the frustum of the cone
$=\frac{1}{3}\mathrm{\pi }h\left[R^2+r^2+Rr\right]{\text{cm}}^3$
$$\begin{gathered} =\frac{1}{3}\times \frac{22}{7}\times 35\times \left[{\left(22\right)}^2+{\left(12\right)}^2+\left(22\times 12\right)\right]{\text{cm}}^3 \\ =\left(\frac{110}{3}\times 892\right){\text{cm}}^3 \\ =\left(\frac{110\times 892}{3\times 1000}\right)\text{litres} \\ =32.7\text{litres} \end{gathered}$$

Hence, the capacity of the bucket is 32.7 litres.