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A rectangular sheet of metal, of area 440 sq.cm is folded into a cylinder, to enclose a volume of 1540 cu.cm. A circle whose diameter is equal to the width of the rectangular sheet is cut from the sheet. Find the ratio of the area of the uncut region to the area of the cut region?

  • math -

    let the radius of the cylinder formed be x cm
    then the length of the rectangle is 2pi(x)
    let the width of the rectangle by y cm

    pi(x^2)(y) = 1540
    2pi(x)(y) = 440
    divide first by second
    x/2 = 3/5
    x = 7

    so area cut out = pi(7)^2 = 49pi
    uncut area = 440 - 49pi

    ratio of uncut:cut
    = (440-49pi)/(49pi)

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