A bucket is in the shape of frustum of a cone. The radii of upper and lower ends of the bucket are 30 cm and 20 cm respectively. The height of the bucket is 38 cm. What is approximate maximum amount of water that the bucket can hold?

It is given that radius of the upper end of the bucket = r₁ = 30 cm

Radius of the lower end of the bucket = r₂­ = 20 cm

Height of the bucket, h = 38 cm

The bucket is in the shape of a frustum of a cone.

Therefore, the volume of the bucket

$=\frac{1}{3}\mathrm{\pi h}\left({{\mathrm{r}}_1}^2+{{\mathrm{r}}_2}^2+{\mathrm{r}}_1{\mathrm{r}}_2\right)$

$=\frac{1}{3}\times \frac{22}{7}\times 38\times \left({30}^2+{20}^2+30\times 20\right)$

$=\frac{22\times 38}{21}\times 1900$

$=75638.095 {\mathrm{cm}}^3$

Thus, the maximum amount of water that the bucket can hold $=\frac{75638.095}{1000}=75.64 L$