Question

The ratio of volumes of two spheres is $8:27$, then the ratio of surface areas is ______

• A. $2:3$
• B. $4:27$
• C. $8:9$
• D. $4:9$

Answer 1

The correct option is D $4:9$

Volume of sphere is $\frac{4}{3}\pi r^3$

$\frac{V_1}{V_2}=\frac{\frac{4}{3}\pi {r_1}^3}{\frac{4}{3}\pi {r_2}^3}=\frac{{r_1}^3}{{r_2}^3}=\frac{8}{27}$

$\Rightarrow \frac{r_1}{r_2}=\frac{2}{3}$

$\Rightarrow \frac{S_1}{S_2}=\frac{4\pi r_1^2}{4\pi r_2^2}=\frac{r_1^2}{r_2^2}={\left(\frac{2}{3}\right)}^2=\frac{4}{9}$