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

We know that

Curved surface area of the tent = area of the cloth $=165m^2$

So we get

$\pi rl=165$

By substituting the values

$\frac{22}{7}\times 5\times 1=165$

On further calculation

$l=\frac{(165\times 7)}{(22\times 5)}=\frac{21}{2}m$

We know that

$h=\sqrt{(l^2-r^2)}$

By substituting the values

$h=\sqrt{\left(\right(21/2{)}^2-5^2)}$

On further calculation

$h=\sqrt{\left(\right(441/4)-25)}=\sqrt{\left(341/4\right)}$

So we get

We know that

Volume of the tent $=\frac{1}{3}\pi r^{2}h$

By substituting the values

Volume of the tent $=\frac{1}{3}\times \frac{22}{7}\times 5^2\times 9.23$

On further calculation

Volume of the tent $=241.7m^2$