Question

The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm. Its volume is
(a) 60060 cm³
(b) 80080 cm³
(c) 70040 cm³
(d) 80160 cm³

Answer 1

(b) 80080 cm³
Let R and r be the radii of the top and base of the bucket, respectively, and let h be its height.

Then,

$R=35\text{cm},r=14\text{cm},h=40\text{cm}$
Volume of the bucket = Volume of the frustum of the cone
$=\frac{1}{3}\mathrm{\pi }h\left[R^2+r^2+Rr\right]{\text{cm}}^3$
$$\begin{gathered} =\frac{1}{3}\times \frac{22}{7}\times 40\times \left[{\left(35\right)}^2+{\left(14\right)}^2+\left(35\times 14\right)\right]{\text{cm}}^3 \\ =\left(\frac{880}{21}\times 1911\right){\text{cm}}^3 \\ =80080{\text{cm}}^3 \end{gathered}$$
Hence, the volume of the bucket is $80080{\text{cm}}^3$.