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      Question

      A cylindrical disc of thickness 1 cm is made by melting

      two solid cylinders of radii 4 cm and 5 cm, and length 6 cm and 4 cm, respectively. The radius of the new cylinder is:
      A 21 cm Correct Answer Incorrect Answer
      B 7 cm Correct Answer Incorrect Answer
      C 14 cm Correct Answer Incorrect Answer
      D 28 cm Correct Answer Incorrect Answer

      Solution

      Cylinder 1: r = 4, h = 6 → V = π × 4² × 6 = 96π Cylinder 2: r = 5, h = 4 → V = π × 5² × 4 = 100π Total volume = 96π + 100π = 196π New disc: height = 1 cm Volume = πR² × 1 = πR² So, πR² = 196π ⇒ R² = 196 ⇒ R = 14

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