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A rectangular sheet of paper 30 cm X 18cm can be transformed into a right circular cylinder in two ways - by rolling the paper along its length or by rolling it along its breadth . Find the ratio of the volume of two cylinders formed.

  • maths -

    rolling along length:
    height = 30, circumference = 18
    2πr = 18
    r = 9/π
    volume = π(81/π^2)(30) = 2430/π

    rolling along breadth
    height = 18
    circumf = 30
    2πr = 30
    r = 15/π
    Volume = π(225/π^2)(18) = 4050/π

    ratio of volume breadth : volume of height
    =(4050/π) : 2430/π
    = 5 : 3

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