Uniformly sized 2-inch sugar cubes are to be packed into boxes, each one measuring 10 × 12 × 15 inches. Packaging “pellets” are to be used to fill any empty space in the box. What is the minimum volume of pellets needed for one box of sugar cubes?

120 cubic inches


The cubes will leave a 1-inch gap at one end of the box’s 15-inch side. The rectangular face at that end measures 10 × 12 inches, and so 120 cubic inches of pellets are required to fill the void.

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