Question

Find the capacity (in $litres$) of a conical vessel with radius $7cm$, slant height $25cm$.
$[Assume\pi =\frac{22}{7}]$

Answer 1

Radius ($r$) of the cone = $7cm$
Slant height ($l$) of the cone = $25cm$
Height ($h$) of the cone $=\sqrt{l^2-r^2}$
$=\left(\sqrt{{25}^2-7^2}\right)cm$
$=24cm$

Volume of cone $=\frac{1}{3}\pi r^{2}h$
$=(\frac{1}{3}\times \frac{22}{7}\times (7{)}^2\times 24)c{m}^3$
$=1232c{m}^3$

Therefore, capacity of the conical vessel
$=\left(\frac{1232}{1000}\right)litres(\because 1litre=1000c{m}^3)=1.232litres$