Question

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

• A. $\frac{3}{4}$
• B. $\frac{1}{4}$
• C. $\frac{1}{5}$
• D. None of these

Answer 1

Answer: (B)

$\frac{1}{4}$

We know, the surface area of a sphere is $4\pi r^2$, where $r$ is the radius.

Let $r_1$ be the original radius and $r_2$ be the new radius.

Then, $r_1=7$ and $r_2=14$.

Therefore, the ratio of the surface area will be:

$=\frac{4\pi r_1^2}{4\pi r_2^2}=\frac{r_1^2}{r_2^2}=\frac{7^2}{{14}^2}=\frac{1}{4}$

Hence, the required ratio is $\frac{1}{4}$.

Therefore, option $B$ is correct.