Question

A cricket ball of radius $r$ fits exactly into a cylindrical tin as shown in the figure below. What will be the ratio between the surface areas of the cricket ball and the tin?

• A. 3:1
• B. 1:2
• C. 2:3
• D. 3:5

Answer 1

The correct option is C

2:3

Given that, the radius of the sphere is $r$.

Since the cricket ball fits exactly inside the cylinder tin, the height of the cylinder ($h$) will be equal to the diameter of the ball .
$\Rightarrow h=2r$

Ratio of their surface areas
$=\frac{Surfaceareaofball}{Surfaceareaofcylindricaltin}$

$=\frac{4\pi r^2}{2\pi r(r+h)}$

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

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

$=\frac{2}{3}$

$=2:3$

Hence, required ratio is 2:3