Passage

Directions: Study the following information carefully and answer the question. The total surface area of a solid cube is 10,584 cm 2 . A sphere of maximum radius is cut out from it. The sphere is cut into eight identical parts by three cuts (one cut along each axis) and the volume of each identical part is (4840 + X) cm 3 . The total surface area of the one identical part is (1720.5 + Y) cm 2 .

If one identical part of the sphere is melted to form 21 small solid cylinders, whose radius is 3.5 cm, then what is the height (in cm) of the solid cylinder?

The total surface area of the cube gives a side length of the square root of 10584 divided by 6, which is 42 cm. The maximum sphere cut from it has a radius of 21 cm, making the volume of each of the eight identical parts one-eighth of 4 thirds times pi times 21 cubed, which equals 4851 cm3. Using the volume conservation formula for melting and recasting, 21 times pi times 3.5 squared times height equals 4851, so the height is 6 cm.

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