Question

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

Answer 1

CSA of cone = area of cloth

$\Rightarrow \pi rl=165$

$\Rightarrow \frac{22}{7}\times 5\times l=165$

$\Rightarrow l=\frac{165\times 7}{22\times 5}=10.5$

$l^2=r^2+h^2\Rightarrow h^2=l^2-r^2$

$\Rightarrow h=\sqrt{l^2-r^2}=9.23cm$

volume = $\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 9.23$

$=241.82c{m}^3$