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A sphere is inscribed in a cube. Find the ratio of volume of sphere to volume of cube. Please give the solution

A sphere is inscribed in a cube. Find the ratio of volume of sphere to volume of cube.
Please give the solution

Grade:11

4 Answers

TANAYRAJ SINGH CHOUHAN
65 Points
7 years ago
Let, Side of Cube = a Therefore, Radius of sphere = a/2(since, sphere touches the two opposite sides of the cube) So, Volume of sphere = 4/3pi.r^3 = 4/3.pi.(a/2)^3 and, Volume of cube = a^3 So, required ratio = {4/3.pi.(a/2)^3}/a^3 = 3pi/2
TANAYRAJ SINGH CHOUHAN
65 Points
7 years ago
Please approve my answer if you like it and best of luck for your preparation.
Shrey
49 Points
7 years ago
The answer is 21:11
SREE NIGAMADITYA NIMMAGADDA
35 Points
7 years ago
the radius of the sphere is equal to 1/2 the side of the cube (since, diameter of the cube is equal to the side of the cube let the radius be `r` then, volume of sphere (V1)=4/3*22/7*r^3 volume of cube (v2)=(2r)^3 the ratio will be equal to v1/v2=22/42 =11/21 that will be equal to 11:21

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