Question

If a sphere and a cube have the same surface area then the ratio of diameter of sphere to edge of cube is:

• A. $\sqrt{6}:\sqrt{\pi }$
• B. $\sqrt{\pi }:\sqrt{6}$
• C. $2:1$
• D. $1:2$

Answer 1

The correct option is A $\sqrt{6}:\sqrt{\pi }$

SA of sphere $=4\pi r^2$
SA of cube $=6a^2$
$\therefore 4\pi r^2=6a^2$
$\Rightarrow \frac{r^2}{a^2}=\frac{6}{4\pi }=\frac{3}{2\pi }$
$\Rightarrow \frac{r}{a}=\sqrt{\frac{3}{2\pi }}$
$\frac{d}{a}=\frac{2r}{a}=2\times \sqrt{\frac{3}{2\pi }}$
$=\frac{\sqrt{2}\times \sqrt{3}}{\sqrt{\pi }}=\frac{\sqrt{6}}{\sqrt{\pi }}=\sqrt{6}:\sqrt{\pi }$