Question

Question 10
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is:

A) 1:4
B) 1:3
C) 2:3
D) 2:1

Answer 1

The answer is A.
Given, radius of a hemispherical balloon, $r_1=6cm$

Air is pumped into the balloon. Then, radius of a hemispherical balloon, $r_2=12cm$

$\therefore$ Ratio of the surface areas of the balloon in two cases $=\frac{3\pi r_1^2}{3\pi r_2^2}$

$\Rightarrow \frac{r_1^2}{r_2^2}=\frac{(6{)}^2}{(12{)}^2}=\frac{36}{144}=\frac{1}{4}=1:4$

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