A sphere is inscribed in a cube. What is the ratio of the volume of the cube to the volume of the sphere?
Let's assume the length of each side of the cube is 'a' and the radius of a sphere 'r'.
When a sphere is inscribed in a cube, then the length of each side of the cube is equal to the diameter of a sphere.
a = 2r  Eq.(i)
The ratio of the volume of the cube to the volume of the sphere =Â $$a^3\ :\ \frac{4}{3}\pi\ r^3$$
Put Eq.(i) in the above equation.
= $$\left(2r\right)^3\ :\ \frac{4}{3}\pi\ r^3$$
= $$8r^3\ :\ \frac{4}{3}\pi\ r^3$$
=Â $$2\ :\ \frac{1}{3}\pi\ $$
=Â $$6\ :\ \pi\ $$
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