If a sphere is inscribed in a cube, then the ratio of the volume of th

1.	If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is :A. π : 2 B. π : 3 C. π : 4 D. π : 6
Answer» Option : (D) Volume of a cube = side³ Volume of a sphere = \(\frac{4}{3}\)πr³ Given, sphere is inscribed in a cube Diameter of sphere = side of the cube Side of cube = 2r Ratio of the volume of the sphere to the volume of cube = \(\frac{\frac{4}{3}\pi r^3}{(2r)^3}\) = π : 6

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is :A. π : 2 B. π : 3 C. π : 4 D. π : 6

Answer»

Option : (D)

Volume of a cube = side³

Volume of a sphere = \(\frac{4}{3}\)πr³

Given,

sphere is inscribed in a cube

Diameter of sphere = side of the cube

Side of cube = 2r

Ratio of the volume of the sphere to the volume of cube

= \(\frac{\frac{4}{3}\pi r^3}{(2r)^3}\)

= π : 6