Question

In Figure 1, the lateral area of the right circular cone is $60\pi$. If the radius of the base is $6$, calculate the volume of the cone.

• A. $96\pi$
• B. $108\pi$
• C. $120\pi$
• D. $184\pi$

Answer 1

The correct option is A $96\pi$

Given, radius of base $=6$

Lateral area of a cone is $\pi rl=60\pi$

$\Rightarrow rl=60$

$\Rightarrow l=\frac{60}{6}$
$\Rightarrow l=10$

$\therefore h=\sqrt{l^2-r^2}=8$
Volume of cone is $\frac{\pi r^{2}h}{3}=96\pi$