Question

The volumes of two spheres are in the ratio of $64:27$. The ratio of their surface areas is __________.

• A. $1:2$
• B. $2:3$
• C. $9:16$
• D. $16:9$

Answer 1

Answer: (D)

$16:9$

Let the volumes of spheres are $V_1$ and $V_2$, and surface areas are $S_1$ and $S_2$.

$\frac{V_1}{V_2}=\frac{r_1^3}{r_2^3}=\frac{64}{27}$ ($\because V=\frac{4}{3}\pi r^3$)

Thus, $\frac{r_1}{r_2}=\frac{4}{3}$

Now, $\frac{S_1}{S_2}=\frac{r_1^2}{r_2^2}$ ($\because S=4\pi r^2$)

$\therefore \frac{S_1}{S_2}=\frac{4^2}{3^2}=\frac{16}{9}$