Question

A cloth having an area of $165m^2$ is shaped into the form of a conical tent of radius $5m$
Find the volume of the cone.

Answer 1

$V=\frac{1}{3}{r}^2\sqrt{A(\frac{A}{r^2}-2\pi )}$

$=\frac{1}{3}{5}^2\sqrt{165(\frac{165}{5^2}-2\frac{22}{7})}$

$=\frac{25}{3}\sqrt{165(\frac{33}{5}-\frac{36}{7})}$

$=\frac{25}{3}\sqrt{165\times \frac{51}{35}}$

$=\frac{25}{3}\sqrt{33\times \frac{51}{7}}$

$=60.25m^3$