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Question
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 ______.
Options
1 : 4
1 : 3
2 : 3
2 : 1
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Solution
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 1 : 4.
Explanation:
Given that radius of a hemispherical balloon (r1) = 6 cm
Since, air is pumped into balloon.
Then, radius of hemispherical balloon (r2) = 12 cm
∴ Ratio of the surface areas of the balloon in both cases = `(3pir_1^2)/(3pir_2^2)`
`\implies r_1^2/r_2^2 = (6)^2/(12)^2`
= `36/144`
= `1/4`
= 1 : 4
Hence, ratio of the surface areas of the balloon in the two cases is 1 : 4.
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