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Math Help - Surface of Revolution

  1. #1
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    Surface of Revolution

    If the curve in the yz-plane with equation z = f(y) is rotated around the y-axis, an equation of the resulting surface of revolution is (A) x2+ z2 = [f(y)]2 , (B) x2+ z2 = f(y), (C) x2+ z2 = |f(y)|, (D) y2 + z2 = |f(y)|, (E) y2 + z2 = [f(x)]2.
    Which of these and why?
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  2. #2
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    Re: Surface of Revolution

    Try to knock out possibilities. At x=0, you are in the yz-plane, and you know that in the plane, you will have z=f(y) and z=-f(y). Plugging in x=0 to B gives z^2=f(y), which must be wrong. C gives z^2=|f(y)|, which is wrong. D is a formula that lies entirely in the yz-plane (so is not a surface of revolution). E rotated the original equation to either to xy- or xz- plane. Hence, A is the only remaining answer.
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  3. #3
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    Re: Surface of Revolution

    Or you could use some geometric intuition to get the answer directly. The distance from the y-axis is f(y), so when it's rotated, \sqrt{x^2+z^2}=f(y).

    - Hollywood
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