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Will a sphere that has the identical surface area as a cube fit inside the cube?

No. The surface of a sphere is 4*pi*r^2, where r is the radius, or pi*d^2, where d is the diameter. The surface of a cube is 6*D^2, where D is the length of any side. If pi*d^2 = 6*D^2, then d = sqrt(6/pi) * D ~ 1.38 * D.

Tim Mooney
Advanced Photon Source, Argonne National Lab.

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