Question

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be

• A. $6:\pi$
• B. $\pi :6$
• C. $12:\pi$
• D. $\pi :2$

Answer 1

The correct option is A $6:\pi$

Let the length of side of cube be $a$.

$\therefore V_1$ (Volume of cube) $=a^3$

Now, Length of side of cube $=$ Diameter of the sphere $=a$

Hence, Radius of sphere $=\frac{a}{2}.$

$V_2$ (Volume of sphere) $=\frac{4}{3}\pi \frac{a^3}{8}$

Ratio of $\frac{V_1}{V_2}=\frac{a^3\times 3\times 8}{4\times \pi \times a^3}$ $=$ $\frac{6}{\pi }$