Question

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

• A. 8 cm
• B. 9 cm
• C. 10 cm
• D. 12 cm
• E. 14 cm

Answer 1

The correct option is C

10 cm

Let the radius and the height of the cone be 3x and 4x respectively.

Then, $\frac{1}{3}\times \pi {3x}^2\times 4x=96\pi \iff 36x^3=(96\times 3)\iff x^3$

=$\left(\frac{96\times 3}{36}\right)$ = 8

$\iff x=2$

Radius = 6 cm, Height = 8 cm

Slant height $=\sqrt{6^2+8^2}cm=\sqrt{100}cm=10cm.$