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The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is

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1:4

1:3

2:3

2:1

answer is A.

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Detailed Solution

Given that, the radius of a hemispherical balloon increases from 6 cm to 12 cm.
We know that,
Total surface area of a hemisphere

= 2 π r^{2} + π r^{2} = 3 π r^{2}

For

r = 6,

Surface area = 3 π × (6) 2 = 36

For

r = 12,

Surface area = 3 π × (12) 2 = 144

So, ratio =

36 : 144

1 : 4

Therefore, the ratio of the surface areas of the balloon in the two cases is 1:4.
Hence option (1) is correct.

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