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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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