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.
Solution and Explanation
Radius (r1) of spherical balloon = 7 cm
Radius (r2) of spherical balloon, when air is pumped into it = 14 cm
\(\text{Required ratio}=\frac{\text{Initial surface area}}{\text{Surface area after pumping air into the balloon}}\)
\(=\frac{4\pi r^2_1}{4\pi r^2_2}\)
\(=(\frac{r_1}{r_2})^2\)
\(=(\frac{7}{14})^2=\frac{1}{4}\)
Therefore, the ratio between the surface areas in these two cases is 1:4.
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