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      Question

      A solid metallic cylinder of radius 5 cm and height 8 cm

      is melted and recast into 10 identical solid cones, each having radius 2 cm. What is the height of each cone?
      A 15 cm Correct Answer Incorrect Answer
      B 33 cm Correct Answer Incorrect Answer
      C 20 cm Correct Answer Incorrect Answer
      D 12 cm Correct Answer Incorrect Answer

      Solution

      ATQ, Volume of cylinder = πr²h = π × 5² × 8 = 200π. Volume of one cone = (1/3)πR²H = (1/3)π × 2² × H = (4/3)πH. For 10 cones: total volume = 10 × (4/3)πH = (40/3)πH. Equating: 200π = (40/3)πH => 200 = (40/3)H => H = 200 × 3 / 40 = 15 cm.

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