Question

Find the ratio of the volume of a cube to that of a sphere which will fit inside it.

Answer 1

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

Since, the sphere exactly fit inside the cube.

∴ Diameter of the sphere = Edge of the cube

$\Rightarrow$ 2r = x

$\frac{Volumeofcube}{Volumeofsphere}$ = $\frac{x^3}{\frac{4}{3}\pi r^3}$ = $\frac{(2r{)}^3}{\frac{4}{3}\pi r^3}$ = $\frac{6}{\pi }$

Thus, ratio of volume of cube: Volume of sphere = 6 :.