Question

Choose the correct answers from the alternatives given.
If a cone, a hemisphere and a cylinder stand on the same base and have height equal to the radius of the base, find out the ratio of their volumes.

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

Answer 1

The correct option is D 1:2:3

Let the radius be r and height be h metres.
Height = Radius
Volume of cone = $\frac{1}{3}\pi r^{2}h$
Volume of cylinder = $\pi r^{2}h$
Volume of sphere = $\frac{2}{3}\pi r^3$
$\frac{1}{3}\pi r^{2}h:\frac{2}{3}\pi r^3:\pi r^{2}h$
$\frac{1}{3}\pi r^2\times r:\frac{2}{3}\pi r^3:\pi r^{2}r$
$\frac{1}{3}\pi r^3:\frac{2}{3}\pi r^3:\pi r^3=1:2:3$