Question

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

• A. 1:3
• B. 2:3
• C. 3:1
• D. 3:2

Answer 1

The correct option is B

2:3

Since the cricket ball exactly fits into the cylindrical tin,

$\therefore$Radius of the cricket ball $=$ Radius of the cylindrical tin $=r$

Also, the height of the cylindrical tin will be equal to the diameter of the ball.
Therefore, $h=2r$
Required ratio $=\frac{\text{Surface area of cricket ball}}{\text{Surface area of the cylindrical tin}}=\frac{4\pi r^2}{2\pi r(r+h)}$

$=\frac{2r}{r+h}=\frac{2r}{r+2r}=\frac{2}{3}$