Question

If a sphere and cube have the same surface are then the ratio of the diameter of sphere to edge of the 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 $\sqrt{6}:\sqrt{\pi }$

Surface area of cube =$6a^2$

Surface area of sphere =$\pi r^2$

As per question both are same

$4\pi r^2=6a^2$

$\Rightarrow \frac{r^2}{a^2}=\frac{3}{2\pi }$

$\Rightarrow \frac{r}{a}=\sqrt{\frac{3}{2\pi }}$

Then ratio of Diameter of sphere and edge of the cube=$\frac{2\sqrt{3}}{\sqrt{2\pi }}=\frac{\sqrt{6}}{\sqrt{\pi }}$