Question

If the ratio of volumes of two spheres is 1 : 8 then the ratio of their surface areas is

• A. 1 : 2
• B. 1 : 4
• C. 1 : 8
• D. 1 : 16

Answer 1

The correct option is B

1 : 4

Violume of first sphere$=\frac{4}{3}\pi r_1^3$

and volume of second sphere $=\frac{4}{3}\pi r_2^3$

But ratio in their volumes = 1 : 8

$\therefore \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}$ $=\frac{1}{8}$

$\Rightarrow \frac{r_1^3}{r_2^3}=\frac{1}{8}={\left(\frac{1}{2}\right)}^3$

$\therefore {\left(\frac{r_1}{r_2}\right)}^3$

$={\left(\frac{1}{2}\right)}^3\Rightarrow \frac{r_1}{r_2}$

$=\frac{1}{2}$

Now ratio in their surfaces areas $=\frac{4\pi r_1^2}{4\pi r_2^2}$

$=\frac{r_1^2}{r_2^2}$

$={\left(\frac{r_1}{r_2}\right)}^2$

$={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$

$\therefore$ Ratio is 1 : 4