Multiple choice

The radius and height of a right circular cone are in the ratio 3 : 4. If its curved surface area (in cm2) is (240 \pi), then its volume (in cm3) is:

  1. $768 π$
  2. $384 π$
  3. $674 π$
  4. $875 π$
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A Correct answer
Explanation

Let radius = 3k, height = 4k. Curved surface area = πrl = 240π, where l = √(r² + h²) = √(9k² + 16k²) = 5k. So π × 3k × 5k = 240π, giving 15k² = 240, so k² = 16, k = 4. Radius = 12, height = 16. Volume = (1/3)πr²h = (1/3)π × 144 × 16 = (1/3)π × 2304 = 768π.

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