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Sphere inside of a Cube : Ratio of Volumes

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A cube has a sphere inscribed inside of it. It has another sphere circumscribed on the outside ot if (it being the cube). What is the ratio of the volume of the inside sphere to the volume of the outside sphere?

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The ratio of volume of a sphere to a cube, where the sphere is inside of the cube, is calculated. The solution is detailed and well presented.

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A cube has a sphere inscribed inside of it
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1) How do I find the ratio of the volume of the inside ...

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