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The radius of a spherical balloon increases from $7$ cm to $14$ cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

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1 : 1

1 : 2

1 : 5

None of these

answer is B.

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Detailed Solution

Given that the radius of a spherical balloon increases from

7

cm to

14

cm as air is being pumped into it.
We know that the surface area of a sphere is

4 π r^{2}

, where

r

is the radius.
Let

r_{1}

be the original radius and

r_{2}

be the new radius.
Then,

r_{1} = 7 cm

and

r_{2} = 14 cm

.
Thus, the ratio of the surface area will be:

⇒ 4 π r 12 4 π r 22 = r 12 r 22 ⇒ 4 π r 12 4 π r 22 = 72142 ⇒ 4 π r 12 4 π r 22 = 12

Therefore, the ratio of surface areas of the balloon in the two cases is 1: 2.
Hence, option (2) is correct.

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