Question

There is a right circular cone of height $h$ and vertical angle ${60}^{\circ }$. A sphere when placed inside the cone, it touches the curved surface and the base of the cone. The volume of sphere is

• A. $\frac{4}{3}\pi h^3$
• B. $\frac{4}{9}\pi h^3$
• C. $\frac{4}{27}\pi h^3$
• D. $\frac{4}{81}\pi h^3$

Answer 1

Answer: (D)

$\frac{4}{81}\pi h^3$

$r=\frac{h}{3}$
$\Rightarrow V=\frac{4}{3}\pi {\left(\frac{h}{3}\right)}^3$
$V=\frac{4\pi .h^3}{81}$.