Question

A right circular cone of vertical height $24cm$ has volume $1232c{m}^3$. Its curved surface area is:

• A. $450c{m}^2$
• B. $500c{m}^2$
• C. $550c{m}^2$
• D. $600c{m}^2$

Answer 1

Answer: (C)

$550c{m}^2$

Given $h=24cmV=1232$ $c{m}^3$.
Volume of cone, $V=\frac{1}{3}\pi r^{2}h$
$\therefore 1232=\frac{1}{3}\times \frac{22}{7}\times r^2\times 24$
$⟹$ $r^2=\frac{1232\times 3\times 7}{22\times 24}=49$
$⟹$ $r=7cm$.

Then, slant height
$l=\sqrt{h^2+r^2}$ $=\sqrt{{24}^2+7^2}=\sqrt{576+49}$ $=25cm$.

Therefore, curved surface area $=\pi rl$
$=\frac{22}{7}\times 7\times 25$ $=550c{m}^2$.

Hence, option $C$ is correct.