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Technically, if the sides are of different lengths, it is a CUBOID, not a cube. The volume of a 4"x3"x2" cuboid is 24 cubic inches.
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Volume of locker: 36*15*14 = 519 cubic inches
Volume of cube = 6*6*6 cubic inches. If the box is h inches high, volume of the box = 8*9*h cubic inches. So 6*6*6 = 8*9*h so h = 6*6*6/(8*9) = 3 inches.
A cone 11 inches high by 4 inches in diameter has a volume of 46.08 cubic inches.