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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
10 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
10 years ago
Please approve my answer if you like it and best of luck for your preparation.
Shrey
49 Points
10 years ago
The answer is 21:11
SREE NIGAMADITYA NIMMAGADDA
35 Points
10 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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