Question

In Figure, the radius of the base of the right circular cone is $3$. If the volume of the cone is $12\pi$, find the lateral area of the cone.

• A. $12\pi$
• B. $15\pi$
• C. $18\pi$
• D. $36\pi$

Answer 1

The correct option is B $15\pi$

Volume of cone with radius $r$ and height $h$ is $=\frac{1}{3}\times \pi r^{2}h$

$=\frac{1}{3}\times \pi (3{)}^{2}h$ $=3\pi h$

But given volume $=12\pi$.

Then, $h=4$.

Given, $r=3$.

Therefore, slant height $l=\sqrt{3^2+4^2}=\sqrt{25}=5$

Hence, Lateral area of cone is $=\pi rl=\pi \times 3\times 5=15\pi$ .

Therefore, option $B$ is correct.