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Homework Help: Volume of Football

  1. Jun 3, 2004 #1
    We have been given the task of finding the volume of a football (elliptical).

    i know the area for an ellipse is [tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

    where a=distance from center to major axis x-direction (Half the length of the ball) (a=14cm)


    b=distance to minor axis y-direction (circumference/2pi) [tex]\frac{73}{2\pi}[/tex]

    from there i get confused. i found on a website that
    i dont understand the Area*dx and where Area= pi*y^2 comes from. Does that mean that pi*y^2 has to be integrated? I also have no idea of how the integration would look like. i do not know what to integrate to get to (pi*b^2/a^2)* ((a^3) - ((a^3)/3)).

    any help would be appreciated greatly. i am confused
  2. jcsd
  3. Jun 3, 2004 #2


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    Science Advisor

    Looking at the football from the skinny end you see a circle.

    You calculate the volume by slicing the football into a bunch of circular slices and finding their volumes. The volume of each slice is the area of the circle, times its thickness. The area of a circle is pi*r2. The thickness is dx. Each slice occurs at a different value of x. The radius of each circle is the y value at that x determined by the equation of the elipse. (actually, it is the seperation of the |y| from the x-axis of the ellipse, but since your ellipse is on the coordinate system x-axis, the y value is that seperation.)

    So, your total volume is the sum of each individual volume which is pi*y2dx.

    You re-arrange your ellipse equation to get y2 in terms of x and integrate.

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