The ratio of the volume of a cube to that of the sphere which exactly fits inside the cube is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(6 : \pi \)
A sphere that fits inside a cube touches all six faces, so its diameter equals the edge of the cube.
Edge of the cube \(=a\), radius of the sphere \(\displaystyle =\frac{a}{2}\)
Volume of the cube \(=a^3\)
Volume of the sphere \(\displaystyle =\frac{4}{3}\pi\left(\frac{a}{2}\right)^3=\frac{\pi a^3}{6}\)
Ratio \(\displaystyle =a^3:\frac{\pi a^3}{6}=6:\pi\)