Correct Answer: 49 : 16

Solution : The surface area of a hemisphere = $3 \pi r^2$
The radius of the balloon before pumping air, $r_1$ = 4 cm
The radius of the balloon after pumping air, $r_2$ = 7 cm
The surface area of the balloon before pumping air, $SA_1$ = $3 \pi r_1^2$
The surface area of the balloon after pumping air, $SA_2$ = $3 \pi r_2^2$
The ratio of the surface areas of the balloon,
= $\frac{SA_2}{SA_1}$
= $\frac{3 \pi r_2^2}{3 \pi r_1^2}$
= $\frac{(r_2)^2}{(r_1)^2}$
= $(\frac{7}{4})^2$
= $\frac{49}{16}$
The ratio of the surface areas of the balloons = 49 : 16
Hence, the correct answer is 49 : 16.