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Question
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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Solution
Radius (r1) of spherical balloon = 7 cm
Radius (r2) of the spherical balloon, when air is pumped into it = 14 cm
Required ratio = `"Initial surface area"/"Surface area after pumping air into a balloon"`
= `(4pir_1^2)/(4pir_2^2)` = `(r_1/r_2)^2`
= `(7/14)^2` = `1/4`
Therefore, the ratio between the surface areas in these two cases is 1 : 4.
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