Multiple choice

Two identical hemispheres of maximum possible size are cut from a solid cube of side 14 cm. The bases of the hemispheres are part of the two opposite faces of cube. What is the total volume (in cm3) of the remaining part of the cube?

  1. 1556.33

  2. 898.5

  3. 1467.33

  4. 1306.67
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D Correct answer
Explanation

The volume of the cube is 14^3 = 2744. Two hemispheres of radius 7 cm make one full sphere of volume (4/3) * pi * 7^3 = (4/3) * (22/7) * 343 = 1437.33. Remaining volume = 2744 - 1437.33 = 1306.67.

AI explanation

The cube volume is 14 cubed, which equals 2744 cubic centimeters. The maximum possible radius for the hemispheres is half the side length, so r equals 7 centimeters. Using the hemisphere volume formula (two thirds pi r cubed), the volume of two such hemispheres is 4 divided by 3 times 22 divided by 7 times 343, which equals 1437.33 cubic centimeters. Subtracting this combined volume from the cube volume gives 1306.67 cubic centimeters.

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