Multiple choice

If a sphere of radius 2 cm is melted to form a cylinder of equal radius, what will be the height of the cylinder?

  1. 2.67 cm

  2. 1.67 cm

  3. 0.67 cm

  4. None of these
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A Correct answer
Explanation

Volume of sphere = 4/3 * pi * r^3 = 4/3 * pi * 8 = 32/3 * pi. Volume of cylinder = pi * r^2 * h = pi * 4 * h. Equating: 32/3 * pi = 4 * pi * h. h = 32/12 = 8/3 = 2.67 cm.

AI explanation

Because the volumes remain equal when the sphere is melted, we equate the volume of the sphere, 4/3 times pi times the radius cubed, to the volume of the cylinder, pi times the radius squared times the height. Substituting the common radius of 2 cm gives 4/3 times pi times 8 = pi times 4 times h. Solving this equation, we get h = 8/3, which is approximately 2.67 cm.

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