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Math Help - radius etc

  1. #1
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    radius etc

    I have a question i need some help on please,

    A factory produces metal discs of radius (r - 1) mm and of negligible thickness for making washers and metal spheres of radius r mm for ball bearings. THe total surface area of a disc (both sides) and a ball bearing is 132 (pie) mm(squared). Calculate r



    thank you
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  2. #2
    Super Member

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    Hello, Kim!

    A factory produces metal discs of radius (r - 1) mm of negligible thickness
    and metal spheres of radius r mm.
    The total surface area of a disc (both sides) and a ball bearing is 132π mm
    Calculate r.
    You're expected to know some area formulas.

    . . Area of circle with radius r: .A .= .πr

    . . Area of sphere with radius r: .A .= .4πr


    The disc has a total area of: .2π(r - 1)

    The sphere has an area of: .4πr


    The total area is 132π: . 2π(r - 1) + 4πr .= .132π

    Divide by 2π: . (r - 1) + 2r .= .66

    We have a quadratic: . 3r - 2r - 65 .= .0

    . . which factors: . (r - 5)(3r + 13) .= .0

    . . and has roots: . r .= .5, -13/3


    Since the radius must be positive: .r = 5

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