Question

A bucket is in the form of a frustum of a cone of height is $30cm$ with radii of its lower and upper ends as $10cm$ and $20cm$ respectively. Find the capacity of the bucket.

Answer 1

Radius of the upper end of the frustum of cone $=R=20cm$
radius of the lower end of the frustum of cone $=r=10cm$
Height $h=30cm$

Volume $=\frac{1}{3}\pi h[R^2+r^2+R\times r]$

$=\frac{1}{3}\times \frac{22}{7}\times 30\times [{20}^2+{10}^2+20\times 10]$

$=\frac{660}{21}\times [400+100+200]$

$=\frac{660\times 700}{21}$

$=22000c{m}^3$

capacity of cone $=$Volume of cone $=22liters$