Question

A right circular cone and a cylinder have a circle of unit radius as base and their heights are equal to the radius itself and a hemisphere has the same radius then their volumes are proportional respectively to

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

Answer 1

The correct option is D 1 : 3 : 2

Let the radius and height of right circular cone , cylinder and himisphere

Then volume of right circular cone=$\frac{1}{3}\pi r^2\times r=\frac{1}{3}\pi r^3$

And volume of cylinder=$\pi r^2\times r=\pi r^3$

And volume of hemisphere=$\frac{2}{3}\pi r^3$

Then ratio =$\frac{1}{3}\pi r^3:\pi r^3:\frac{2}{3}\pi r^3=1:3:2$