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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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#### Solution

Radius (*r*_{1}) of spherical balloon = 7 cm

Radius (*r*_{2}) of spherical balloon, when air is pumped into it = 14 cm

`"Required ratio "="Initial surface area"/"Surface area after pumping air into 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.

Concept: Surface Area of a Sphere

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