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Thread: Finding the volume of an ellipse watermelon

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    Finding the volume of an ellipse watermelon

    An ellipse watermelon has a major axis 28cm and minor axis 25cm. The equation of the ellipse is y = 12.5 - 12.5x/145 Find the volume using calculusJust wondering if anyone can help me out on this question! I'm not quite sure how to answer it as I keep getting an abnormally large number.Thanks!
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    Re: Finding the volume of an ellipse watermelon

    An ellipse watermelon has a major axis 28cm and minor axis 25cm. The equation of the ellipse is y = 12.5 - 12.5x/145
    ?

    $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$

    assuming the major axis is along the x-axis, $a=14$ and $b=\dfrac{25}{2}$ ...

    $\dfrac{x^2}{196}+\dfrac{4y^2}{625} = 1$

    $y^2 = \dfrac{625}{4}\left(1-\dfrac{x^2}{196}\right)$

    V = 2\pi \int_0^{14} \dfrac{625}{4}\left(1-\dfrac{x^2}{196}\right) \, dx

    V = \dfrac{625\pi}{2} \int_0^{14} \left(1-\dfrac{x^2}{196}\right) \, dx = \dfrac{8750\pi}{3}
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    Re: Finding the volume of an ellipse watermelon

    If the question is asking in terms of the solid of revolution, would the x-axis be 12.5 not 14? Hence changing the dimensions of the integration??
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    Re: Finding the volume of an ellipse watermelon

    Finding the volume of an ellipse watermelon-screen-shot-2017-07-11-12.55.57-pm.png
    Click image for larger version. 

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    Does this diagram make sense or does it need to be around the other way?? And I also thought that it was considering the whole ellipse not half? I'm a bit confised sorry...
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    Re: Finding the volume of an ellipse watermelon

    I centered the ellipse at the origin. I don't think I've ever seen a watermelon looking like it was a solid of revolution about its minor axis.



    The integral set up takes advantage of symmetry w/respect to the y-axis.

    $\displaystyle \pi \int_{-14}^{14} [r(x)]^2 \, dx = 2\pi \int_0^{14} [r(x)]^2 \, dx$

    note $[r(x)]^2 = y^2$
    Attached Thumbnails Attached Thumbnails Finding the volume of an ellipse watermelon-img_1628.png  
    Last edited by skeeter; Jul 11th 2017 at 08:43 AM.
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