The radius of a spherical balloon increases from 7 cm to 14 cm as air is jumped into it. Find the ratio of the surface areas of the balloon in two cases.

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The radius of a spherical balloon increases from 7 cm to 14 cm as air is jumped into it. Find the ratio of the surface areas of the balloon in two cases.

Solution:

Given radius of the spherical balloon, r = 7 cm

Radius of the spherical balloon after air is pumped, R = 14 cm

Surface area of the sphere = 4r²

Ratio of surface areas of the balloons = 4r²/4R²

= r²/R²

= 7²/14²

= 1/4

Hence the ratio of the surface areas of the spheres is 1:4.