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Math

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If the radius of a circle is increased by 1 unit, the area of the circle is increased by 16 pi square units. What is the radius of the original circle?

  • Math - ,

    original radius --- r
    new radius ------ r+1

    original area = πr^2
    new area = π(r+1)^2

    π(r+1)^2 - πr^2 = 16π
    divide by π and expand ...
    r^2 + 2r + 1 - r^2 = 16
    2r = 15
    r = 7/5 units

    check:
    old area = π(7.5)^2 = 56.25π
    new area = π(8.5)^2 = 72.25π
    difference = 72.25P - 56.25π = 16π
    all looks good!

  • Math - ,

    AMAZING. Thanks Much.

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