Question

A sphere circumscribes a cube of side '$a$'. How many times the volume of cube is the volume of the sphere ?

• A. $2$
• B. $\pi$
• C. $\frac{\pi \sqrt{3}}{2}$
• D. $\sqrt{3}$

Answer 1

Answer: (C)

$\frac{\pi \sqrt{3}}{2}$

If edge of cube $=$ a, diameter of sphere
$=a\sqrt{3}$ and radius $=a\sqrt{3}/2$
Therefore, volume of sphere $=\frac{4}{3}\pi {\left(\frac{a\sqrt{3}}{2}\right)}^3=\frac{4}{3}\pi \times \frac{3\sqrt{3}}{8}\times a^3$
$=\pi \frac{\sqrt{3}}{2}\times a^3=\frac{\pi \sqrt{3}}{2}\times \text{volume of cube}$