Sphere Sandwich

Geometry Level 4

We begin with a cube \(C_1\).

Inside this cube \(C_1\) we fit a sphere \(S\), which touches the cube in the midpoint of each of the six faces.

Inside the sphere \(S\) we fit a smaller cube \(C_2\), whose eight vertices touch the sphere.

Express the volume of cube \(C_2\) as a percentage of the volume of \(C_1\). Round off to a whole number.


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