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Q.

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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a

    1:4

b

    1:3

c

    2:3

d

    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 =2πr2+πr2=3πr2 For r=6, Surface area=3π× (6) 2 =36  
For r=12,
Surface area=3π× (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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