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Math Help - Surface Area of a solid on a graph?

  1. #1
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    Surface Area of a solid on a graph?

    For this question: http://i62.tinypic.com/2uh70xw.jpg I've been stuck for a while. I'm used to finding area using a cross section but is my surface area answer right? I'm not sure about it (Just for participation points, doesn't count if I get it right but I want to know if I'm doing it right) Can you take me through the steps and did I come up with the right answer?
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  2. #2
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    Re: Surface Area of a solid on a graph?

    I think it's similar to calculating arc length. The surface area of a small slice of width dx is 2 \pi y \sqrt {1 + (y')^2} \, dx. You have y = \sqrt{2x} and y' = - \frac{1}{\sqrt{2x}}. So you integrate \int_0^2 2\pi \sqrt{2x} \sqrt{1+\frac{1}{2x}} \, dx, which comes out to 21.322.

    - Hollywood
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  3. #3
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    Re: Surface Area of a solid on a graph?

    Quote Originally Posted by hollywood View Post
    I think it's similar to calculating arc length. The surface area of a small slice of width dx is 2 \pi y \sqrt {1 + (y')^2} \, dx. You have y = \sqrt{2x} and y' = - \frac{1}{\sqrt{2x}}. So you integrate \int_0^2 2\pi \sqrt{2x} \sqrt{1+\frac{1}{2x}} \, dx, which comes out to 21.322.

    - Hollywood
    Thank you Hollywood!
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