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Math Help - Volume around the y-axis

  1. #1
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    Volume around the y-axis

    Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y = x^2 and y = 9 about the y axis.


    My first answer was 54, my second 18. Neither are correct, but I feel at a loss for this problem.
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  2. #2
    Senior Member eumyang's Avatar
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    Have you learned the disk method for finding a volume of a solid of revolution? You have a vertical axis of revolution so you'll have to rewrite the function y = x^2 in terms of x -> x = \sqrt{y}.

    The integral to set up is
    V = \pi \displaystyle \int_c^d [R(y)]^2 dy

    Plug in \sqrt{y} for R(y), 0 for c, and 9 for d:

    V = \pi \displaystyle \int_0^9 (\sqrt{y})^2 dy

    Take it from here.
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  3. #3
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    I had not learned this method (or many others). I'm in the process of teaching myself Calc I out of a textbook and so I'm having a hard time connecting some of the dots. Let me work this real quick...127.23.

    Thank you!
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