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    Question

    The radius of a cylinder is increased by 20%, and its

    height is decreased by 10%. Find the percentage change in the volume of the cylinder.
    A 25.2% increase Correct Answer Incorrect Answer
    B 27.6% increase Correct Answer Incorrect Answer
    C 29.6% increase Correct Answer Incorrect Answer
    D 22% increase Correct Answer Incorrect Answer

    Solution

    Let the initial radius be r and height be h. The initial volume is: VтВБ = ╧Аr┬▓h. New radius = 1.2r, new height = 0.9h. New volume: VтВВ = ╧А(1.2r)┬▓(0.9h) = ╧А(1.44r┬▓)(0.9h) = ╧Аr┬▓h ├Ч 1.296. Percentage change in volume: [(VтВВ - VтВБ)/VтВБ] ├Ч 100 = [(1.296VтВБ - VтВБ)/VтВБ] ├Ч 100 = 29.6%. Correct answer: c. 29.6% increase

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