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Solution: What volume inside the spherical shell not occupied by the cubical block?

What volume inside the spherical shell is not occupied by the cubical block?

Problem Statement: CE Board May 1997

The corners of a cubical block touched the closed spherical shell that encloses it. The volume of the box is 2744 cubic cm. What volume in cubic centimeters inside the shell is not occupied by the block?

Problem Answer:

The volume inside the spherical shell not occupied by the cubical block is 4713.56 cu. cm.

Solution:

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