Easier to figure using the radius rather than the diameter. Volume of the sphere is 4pi/3 * r^3, volume of the cube is (2r)^3. Factor out r^3 and you get (4pi

Easier to figure using the radius rather than the diameter. Volume of the sphere is 4pi/3 * r^3, volume of the cube is (2r)^3. Factor out r^3 and you get (4pi/3)/8, or 52% of the cube's volume is within the sphere.