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Math Help - change in volume

  1. #1
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    change in volume

    The radius of cylinder is reduced by 4% and its height is increased by 2%, determine the approximate percentage changed in (i) its volume (ii) its curved surface area (neglecting the product of small quantities)
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  2. #2
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    Hello, Gracy!

    I'll assume that this is to be done by Arithmetic . . .


    The radius of cylinder is reduced by 4% and its height is increased by 2%.
    Determine the approximate percentage changed in (i) its volume
    (ii) its curved surface area (neglecting the product of small quantities)

    Let r be the original radius, then 0.96r is the new radius.
    Let h be the original height, then 1.02h is the new height.

    The original volume is: .V1 .= .πrh

    The new volume is: .V2 .= .π(0.96r)(1.02h) . .(0.94)πrh

    The change in volume is: .V1 - V2 .= .πrh - (0.94)πrh .= . (0.06)πrh


    . . . . . . . . . . . . . . . . .change . . . (0.06)πrh
    Percent of change . = . --------- .= .------------- .= .0.06 .= .6%
    . . . . . . . . . . . . . . . . .original . . . . .πrh


    You can do part (ii).
    The curved surface area is: .S .= .2πrh

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