A sphere is inscribed in a cube. What is the ratio of the volume of the cube to the volume of the sphere?
Answer & explanation
Correct answer: option 1
We know that,
Volume of sphere = \(\frac{4}{3}\)πr3
Let, Side of cube = x
then, Volume of cube = x3
Radius of sphere r = \(\frac{x}{2}\)
Volume of sphere = \(\frac{4}{3}\) π × \(\frac{x}{2}\)3 = \(\frac{x^3}{6}\)π
Volume of cube : Volume of sphere = x3 : \(\frac{x^3}{6}\)π = 6 : π