Question

If a sphere is inscriped in a cube, then find the ratio of volume of the sphere

Answer 1

Diameter of sphere = edge of cube
let radius of sphere be x units
therefore edge of cube = 2x units
volume of cube = a³
= (2x)³ = 8x³
volume of sphere = 4/3 π r³
=4/3×22/7×x³
=88x³/21

therefore
volume of cube/volume of sphere
=8x³/88x³/21×21/21=168x³/88x³
=21/11
therefore the ratio of cube's volume to sphere's volume is 21:11

Answer 2

Answer:

Surface area of a cube of edge 'a' units = 6a2 sq units

Surface area of a sphere = 4πr2 sq units

Given that, 6a2 = 4πr2

⇒ a = [2r√π] / √6

⇒ a3 = [8πr3√π] / 6√6

Volume of the sphere = 4 3 πr3 cu units

Volume of the cube = a3 cu units

Ratio of volumes = [4 3 πr3] / [a3]

= [4 3 πr3] / [(8πr3√π) / 6√6]

= √6 : √π

Therefore, the ratio of the volumes of the sphere and the cube is √6 : √π.