Question

Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

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

Answer 1

The correct option is B

$6:\pi$

Let the radius of the sphere which fits exactly into the cube be $r$ units. Then, length of each edge of the cube$=2r$ units.
Let $V_1$ and $V_2$ be the volume of the cube and sphere respectively.
Then,
$V_1={\left(2r\right)}^3$ and $V_2=\frac{4}{3}\pi r^3$
$\therefore \frac{V_1}{V_2}=\frac{8r^3}{\frac{4}{3}\pi r^3}=\frac{6}{\pi }\Rightarrow V_1:V_2=6:\pi$.