Question

The radius and height of a right circular cone are in the ratio $3:4$. If its volume is $96\pi c{m}^3$, what is its slant height?

• A. $8$cm
• B. $9$cm
• C. $10$cm
• D. $12$cm

Answer 1

The correct option is C $10$cm

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

Given, ratio of radius and height $=3:4$.

Let $h=4x$ and $r=3x$.

Then,

$V=\frac{1}{3}\times \pi \times 9x^2\times 4x=12\pi x^3$.

Also given, volume $V=96\pi c{m}^3$.

Thus,

$x^3=8$

$\Rightarrow x=2$.

$\therefore$ Slant height $l=\sqrt{h^2+r^2}=\sqrt{25x^2}=5x=10cm$.

Hence, option $C$ is correct.