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      Question

      If the radius of a right circular cylinder open at both

      the ends, is decreased by 25% and the height of the cylinder is increased by 25%. Then the curved surface area of the cylinder thus formed
      A remains unaltered Correct Answer Incorrect Answer
      B is increased by 25% Correct Answer Incorrect Answer
      C is increased by 6.25% Correct Answer Incorrect Answer
      D is decreased by 6.25% Correct Answer Incorrect Answer

      Solution

      Curved suface area of cylinder = 2 πrh
      New radius of the cylinder = r × (75/100) = 0.75r
      New height of the cylinder = h × (125/100) = 1.25h
      Curved surface area of new cylinder = 2 π × 0.75r × 1.25h
      Taking ratio of C.S.A before to after = 2 πrh : 2 π × 0.75r × 1.25h = 1 : 0.9375
      Let C.S.A before be 1 and after C.S.A be 0.9375
      C.S.A decrased by = 1 – 0.9375 = 0.0625
      ∴ C.S.A decresed by (in %) = 0.0625/1 × 100 = 6.25%

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