Question

The radius of a hemispherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratios of the surface areas of the balloon in the two cases.

Answer 1

When $r=7$ $cm$

$S_1=3\pi r^2=3\pi \times 7^2$

When $r=14$ $cm$

$S_2=3\pi \times {14}^2$

Therefore,

$\frac{S_1}{S_2}=\frac{7\times 7}{14\times 14}$

$\frac{S_1}{S_2}=\frac{1\times 1}{2\times 2}$

$S_1:S_2=1:4$