# 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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