Question

A bucket is in the form of frustum of cone and holds $28.490$ litres of water. The radii of the top and bottom are $28$ cm and $21$ cm respectively. Find the height of the bucket.

Answer 1

Given : Volume $=28.490$ litres $=28490{cm}^3$
Radius of the top of cone $=r_1=28$ cm.
Radius of the bottom of cone $=r_2=21$ cm.
Find : The height of the bucket.
Volume of frustrum $=\frac{1}{3}\pi (r_1^2+r_2^2+r_1\times r_2)h$
$\therefore 28490=\frac{1}{3}\times \frac{22}{7}\times ({28}^2+{21}^2+28\times 21)\times h$
$\therefore 28490=\frac{22}{21}\times (784+441+588)\times h$
$\therefore h=\frac{28490\times 21}{22\times 1813}=15$ cm.
$\therefore$ height of the bucket $=15$ cm.