Question

The radius of a sphere is r and radius of base of a cylinder is r and height is 2r. The ratio of their volumes will be-

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

Answer 1

The correct option is A $2:3$

Given,

The radius of the sphere $=r$

The radius of the cylinder $=r$

The height of the cylinder $=2r$

We know that the volume of the sphere

$V_1=\frac{4}{3}\pi r^3$

We know that the volume of the cylinder

$V_2=\pi r^{2}h$

$V_2=\pi r^2\left(2r\right)$

$V_2=2\pi r^3$

Therefore, the required ratio

$\frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r^3}{2\pi r^3}$

$\frac{V_1}{V_2}=\frac{2\pi r^3}{3\pi r^3}$

$\frac{V_1}{V_2}=\frac{2}{3}$

$V_1:V_2=2:3$

Hence, this is the answer.