Question

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket.$[Use=\frac{22}{7}]$

Answer 1

Let the height of the bucket be h cm.
Suppose $r_1$ and $r_2$ be the radii of the circular ends of the bucket.
Given, $r_1=28$ cm and $r_2=21cm$
Capacity of bucket = 28.49 litres
$\therefore$ Volume of the bucket =$28.49\times 1000c{m}^3$[1 litre =1000 $c{m}^3]$
$\Rightarrow \frac{1}{3}\pi h(r_1^2+r_2^2+r_1{r}_2)=28.49\times 1000c{m}^3\Rightarrow \frac{1}{3}\times \frac{22}{7}\times h(28{)}^2+(21{)}^2+(28\times 21)c{m}^2=28490c{m}^3\Rightarrow \frac{22}{21}\times h\times 1813=28490cm\Rightarrow h=\frac{28940\times 21}{22\times 1813}\Rightarrow h=15cm$
Thus, the height of the bucket is 15 cm.