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.

• A. $241.74m^2$
• B. $240m^2$
• C. $250.48m^2$
• D. $260m^2$

Answer 1

The correct option is A $241.74m^2$

Curved surface area of cone $=165$ m${}^2$

$\Rightarrow \pi rl=165$

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

$\Rightarrow l=10.5$ m

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

$\Rightarrow h=\sqrt{{10.5}^2-5^2}$

$\Rightarrow h=9.23$ m

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

$\therefore V=\frac{1}{3}\pi {\times 5}^2\times 9.23=241.74$ m${}^2$