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Math Help - Volume

  1. #1
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    Volume

    As viewed from above, a swimming pool has the shape of the ellipse given by

    The cross sections perpendicular to the ground and parallel to the -axis are squares. Find the total volume of the pool.
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    Quote Originally Posted by amiv4 View Post
    As viewed from above, a swimming pool has the shape of the ellipse given by

    The cross sections perpendicular to the ground and parallel to the -axis are squares. Find the total volume of the pool.
    note that the the curve is given by y = \pm \sqrt{2500 - \frac {25x^2}{49}}

    the plus part gives the curve above the x-axis, the minus part gives the curve below the x-axis.

    recall, the volume is given by

    V = \int_a^b A(x)~dx

    where A(x) is the cross-sectional area.

    note that here, A(x) is given by the formula for a square, where the side length is given by the difference between the two functions.
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    so is A(x) = x^2
    im confused on that part
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    Quote Originally Posted by amiv4 View Post
    so is A(x) = x^2
    im confused on that part
    i told you, the height of the square is the difference between the two functions. draw any vertical line in the ellipse that connects the top to the bottom. the length of that line is the side length of the square at that point. it's length is given by the difference of the functions
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  5. #5
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    so A(x) = (sqrt(2500-25x^2/49)-(-sqrt(2500-25x^2/49)))^2
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    Quote Originally Posted by amiv4 View Post
    so A(x) = (sqrt(2500-25x^2/49)-(-sqrt(2500-25x^2/49)))^2
    yes, but of course you can simplify that a lot. who'd want to integrate that thing?!
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    is it integrated from 0 to 1
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    Quote Originally Posted by amiv4 View Post
    is it integrated from 0 to 1
    no

    look at the graph, or better yet, solve for the x-intercepts of your functions. you realize that those will be your limits of integration, right?
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    so it would be from -70 to 70
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    Quote Originally Posted by amiv4 View Post
    so it would be from -70 to 70
    yes
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  11. #11
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    k well i put that in my calculator and got 933333.3333 and that isnt right so idk what else im not doing. Did u get something close to that
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    Quote Originally Posted by amiv4 View Post
    k well i put that in my calculator and got 933333.3333 and that isnt right so idk what else im not doing. Did u get something close to that
    that is what i got

    we can check to see if we missed something
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  13. #13
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    oh ok i just forgot one of the 3's when i put it in. so it works now. Thanks
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