Question

The radii of two sphere are in the ratio $3:4$. The ratio of their surface area is:

• A. $3:16$
• B. $4:16$
• C. $6:16$
• D. $9:16$

Answer 1

The correct option is D $9:16$

Given, the ratio of radii of two spheres is $3:4$.

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

Let $r_1$ and $r_2$ be the radii of the two sphere,

i.e. $r_1:r_2=\frac{r_1}{r_2}=3:4=\frac{3}{4}$.

Then, the areas of the spheres be $4\pi r_1^2$ and $4\pi r_2^2$.

Therefore, the ratio of their surface area

$=\frac{4\pi r_1^2}{4\pi r_2^2}=\frac{r_1^2}{r_2^2}=(\frac{r_1}{r_2}{)}^2=(\frac{3}{4}{)}^2=\frac{9}{16}=9:16$.

Hence, option $D$ is correct.