Multiple choice

A cylinder whose height is 2/3 of its diameter has same volume as that of a sphere of radius 8 cm .The radius of base of the cylinder is

  1. 8 cm

  2. 4 cm

  3. 2 cm

  4. None of these
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A Correct answer
Explanation

Volume of sphere = (4/3) * pi * 8^3 = 2048/3 * pi. Cylinder height h = (2/3) * 2r = 4r/3. Volume of cylinder = pi * r^2 * h = pi * r^2 * (4r/3) = 4/3 * pi * r^3. Equating volumes: 4/3 * pi * r^3 = 4/3 * pi * 8^3, so r = 8.

AI explanation

By equating the volumes using pi * r^2 * h = (4/3) * pi * R^3, where the cylinder's height is 2/3 of its diameter (h = 4r/3), we get pi * r^2 * (4r/3) = (4/3) * pi * 8^3. This simplifies to r^3 = 8^3, giving a cylinder radius of 8 cm.

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