1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)

    and

    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

    Njorl

    User Avatar
    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.

    Njorl
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Volume of Football
  1. Height of football (Replies: 4)

  2. Impulse for a football (Replies: 1)

  3. Football kick (Replies: 2)

  4. Football Question. (Replies: 4)

  5. Football Kinematics (Replies: 13)

Loading...