Question

The value of a sphere is $\frac{4}{3}\pi r^{3}c.c.$ What is the ratio of the volume of a cube to that of a sphere which will fit inside the cube?

• A. $4:3\pi$
• B. $2:\pi$
• C. $8:\pi$
• D. $6:\pi$

Answer 1

Answer: (D)

$6:\pi$

Given, Volume of the sphere $=\frac{4}{3}\pi r^3$

Volume of the cube $=a^3$

For a sphere to fir in the cube it's radius should be equal to $\frac{a}{2}$

Therefore, the required ratio

$=\frac{a^3}{\frac{4}{3}\pi \frac{a^3}{8}}$

$=\frac{6}{\pi }$

$=6:\pi$

Hence, this is the answer.