Multiple choice

Two solid cylinders are $12\;cm\;and\;18\;cm$ in height. Their diameters are $12\;cm\;and\;16\;cm$ respectively. Both the cylinders are melted and the material is moulded into a solid right circular cone of height $33\;cm$. Find its diameter.

  1. $28\;cm$
  2. $20\;cm$
  3. $14\;cm$
  4. $24\;cm$
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D Correct answer
Explanation

Volume of cylinder 1 = pi * 6^2 * 12 = 432pi. Volume of cylinder 2 = pi * 8^2 * 18 = 1152pi. Total volume = 1584pi. Cone volume = (1/3) * pi * r^2 * 33 = 11 * pi * r^2. 11 * r^2 = 1584 => r^2 = 144 => r = 12. Diameter = 24 cm.

AI explanation

The total volume of the two cylinders is found using V = pi * r^2 * h, yielding pi * 6^2 * 12 + pi * 8^2 * 18 = 432pi + 1152pi = 1584pi. Setting this equal to the volume of the cone with height 33 cm gives (1/3) * pi * R^2 * 33 = 1584pi. Solving for R, the radius of the cone is 12 cm, so its diameter is 24 cm.

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