Question

The volume 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

The correct option is D $6:\pi$

Let the edge of the cube and radius of the sphere be $x$ and $r$ units respectively.

Since the sphere exactly fit inside the cube, therefore diameter of sphere is equal to edge of the cube that is $2r=x$.

Now consider volume of cube over volume of sphere:

$\frac{x^3}{\frac{4}{3}\pi r^3}=\frac{{\left(2r\right)}^3}{\frac{4}{3}\pi r^3}=\frac{8r^3}{\frac{4}{3}\pi r^3}=\frac{2}{\frac{1}{3}\pi }=\frac{2\times 3}{\pi }=\frac{6}{\pi }$

Hence, the ratio is $6:\pi$.