If a sphere is inscriped in a cube, then find the ratio of volume of the sphere
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8
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
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
Answered by
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.
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