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A sphere is inside a cube.The diameter of the sphere is equal to the edge length of the cube. What portion of the volume of the cube is taken up by the sphere?

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Answer: if a cube is inscribed inside a sphere then the diagonal (longest side) of the cube is equal to the diameter of the sphere?

the formula for diagonal of a cube is D = 3√3a

Explanation:

A cube is inscribed inside a sphere then the diagonal (longest side) of the cube is equal to the diameter of the sphere the formula for diagonal of a cube is D = 3√3a.

How do you find The volume of a cube with a sphere inside?

If s is the side length of the cube, then Vcube=s3.

look that the largest possible sphere that can fit inside the cube is the inscribed sphere, which has radius 12s.

Using the volume formula for a sphere, we find that Vsphere=43πr3=43πs38=π6s3.

Thus,  the diameter of the sphere the formula for diagonal of a cube is D = 3√3a.

To learn more about cube click here:

https://brainly.com/question/15420947

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