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

Surface area of sphere = 4πr².

Given, radius in 1st case = 7 cm and in 2nd case = 14 cm.

$\dfrac{\text{Surface area in 1st case}}{\text{Surface area in 2nd case}} = \dfrac{4 \times π \times (7)^2}{4 \times π \times (14)^2} \\[1em] = \dfrac{7 \times 7 }{14 \times 14} \\[1em] = \dfrac{49}{196} \\[1em] = \dfrac{1}{4}$

Hence, the ratio of the surface areas of the balloon in two cases is 1 : 4.