A cube has an edge length of 72 inches. A solid sphere with a radius of 36 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

Calculate the volume of the space inside a cube with an edge length of 72 inches that is not occupied by a sphere inscribed within it. Learn the formulas for volumes of cubes and spheres, and understand the geometric relationship between a cube and an inscribed sphere. Suitable for high school students studying solid geometry.

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