Question

A canvas of area 550 m${}^2$ is used to make a tent of radius 7 m. The volume of that tent =

• A. 1232 m${}^3$
• B. 3850 m${}^3$
• C. 2257 m${}^3$

Answer 1

The correct option is A 1232 m${}^3$

From the given data, CSA of cone = 550m${}^2$
Therefore $\pi rl$ = 550m${}^2$
$\Rightarrow \frac{22}{7}\times 7\times l=550m^2$
$\Rightarrow l=\frac{550}{22}=25m$
$\because l^2=r^2+h^2\therefore h=\sqrt{{25}^2-7^2}=\sqrt{576}=24m$

Volume of the tent $=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24$
$=1232m^3$