A cricket ball of radius r fits exactly into a cylindrical tin as shown in the f

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?

Options:

A . 1:2

B . 2:3

C . 3:1

D . 3:5

Answer: Option B
:
B
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 = 2 r

Ratio of their surface areas

= \frac{S u r f a c e a r e a o f b a l l}{S u r f a c e a r e a o f c y l i n d r i c a l t i n}

= \frac{4 π r^{2}}{2 π r (r + h)}

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

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

= \frac{2}{3}

= 2 : 3

Hence, required ratio is 2:3

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