Question

$\text{If the ratio of the volumes of two spheres is 1:8 then ratio of their surface areas is}\left(a\right)1:2\left(b\right)1:4\left(c\right)1:8\left(d\right)1:16$

Answer 1

ANSWER:
(b) 1 : 4
Suppose that r and R are the radii of the spheres.
Then we have:
$\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\frac{1}{8}$
⇒$(\frac{r}{R}{)}^3=\frac{1}{8}$

⇒$\frac{r}{R}=\frac{1}{2}$
∴ Ratio of surface area of spheres = $\frac{4\pi r^2}{4\pi R^2}=(\frac{r}{R}{)}^2=\frac{1}{4}$