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  1. #1
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    cylinder

    A cylindrical concrete sewer pipe is to be cast so that the concrete is uniformly 75mm thick while the cross section of the concrete is 0.164m^2.
    formulate and solve the simultaneous equations showing the relationship between the external radius R and the internal radius r of the pipe.
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  2. #2
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    Quote Originally Posted by zak_killcity14@hotmail.co View Post
    A cylindrical concrete sewer pipe is to be cast so that the concrete is uniformly 75mm thick while the cross section of the concrete is 0.164m^2.
    formulate and solve the simultaneous equations showing the relationship between the external radius R and the internal radius r of the pipe.
    The cross-sectional area is simply the area of the circle of external radius R with the area of the circle of internal radius r subtracted. So:
    0.164 = (pi)(R^2 - r^2)

    We also know that
    0.075 = R - r

    Thus: R = 0.075 + r

    Inserting this into the first equation:
    0.164 = (pi)([0.075 + r]^2 - r^2)

    0.164 = (pi)(0.150r + 0.005625)

    Which you can solve for r. Then you can use that value of r in the R = 0.075 + r equation to get R.

    I get r = 0.311 m and R = 0.386 m (or so.)

    -Dan
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