Question

The radii of two circular ends of a frustum shaped bucket are $15\text{cm}$ and $8\text{cm}$. If its depth is $63\text{cm}$, find the capacity of the bucket in litres. (Take $\pi =\frac{22}{7}$)

Answer 1

Let $R$ and $r$ are radii of the circular ends at the top and bottom and $h$ be the depth of the bucket respectively.
Given that $R=15\text{cm},r=8\text{cm}$ and $h=63\text{cm}$
The volume of the bucket (frustum)
$=\frac{1}{3}\pi (R^2+r^2+Rr)\times h$
$=\frac{1}{3}\times \frac{22}{7}\times 63\times ({15}^2+8^2+15\times 8)=29664{\text{cm}}^3$
$=\frac{26994}{1000}$ litres $[\because 1000{\text{cm}}^3=1$ litre$]$
Thus, the capacity of the bucket $=26.994$ litres.