Question

If the volume and the base area of a right circular cone are $48\pi {cm}^3$ and $12\pi {cm}^2$ respectively, then the height of the cone is equal to:

• A. $6cm$
• B. $8cm$
• C. $10cm$
• D. $12cm$

Answer 1

The correct option is D $12cm$

We have,

Volume $=48\pi c{m}^3$

Base area $=12\pi c{m}^2$

We know that the volume of the cone

$V=\frac{1}{3}\pi r^{2}h$

We know that the base area of the cone

$A=\pi r^2$

So,

$\frac{1}{3}\pi r^{2}h=48\pi$

$⟹$ $\frac{1}{3}\left(\pi r^2\right)h=48\pi$

$⟹$$\frac{1}{3}\times 12\pi h=48\pi$ $\left[given\right]$

$⟹$$4\times h=48$

$⟹$$h=12cm$.

Hence, option $D$ is correct.