Question

A cricket ball of radius $r$ is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of cricket ball to the total surface area of the cylindrical tin is

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

Answer 1

The correct option is B

$2:3$

As the cricket ball is exactly fitted in a cylindrical tin,

the height of cylinder $\left(h\right)$ will be equal to the diameter $\left(2r\right)$ of the ball and radius of ball = radius of cylinder.
Therefore, $h=2r$
Ratio of their areas $=\frac{4\pi r^2}{2\pi r(r+h)}=\frac{2r}{r+h}=\frac{2r}{r+2r}=\frac{2}{3}$