Question

A cylinder is circumscribed about a hemisphere and a cone is inscribed in the hemisphere such that its base coincides with the base of hemisphere. The volume of cylinder, volume of hemisphere and the volume of cone are proportional to

• A. 4 : 3 : 2
• B. 2 : 3 : 1
• C. 1 : 2 : 3
• D. 3 : 2 : 1

Answer 1

The correct option is D 3 : 2 : 1

Clearly h=r
Volume of cylinder : Volume of semispheres :volume of cone
$=\pi \left(r^2\right)r:\frac{2}{3}\pi r^3:\frac{1}{3}\pi r^2\left(r\right)=3:2:1.$