Results 1 to 2 of 2

Math Help - volume of a spherical cap

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    4

    volume of a spherical cap

    i need help finding the volume of a spherical cap. the only information i know is that the rim of the cap is 5m and its height is 2m.

    I have tried integrating using the formula for a sphere but the problem is I don't know the radius of the sphere from which the cap came and I can't figure out where to go from there. please help. thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Feb 2008
    Posts
    410
    Quote Originally Posted by justonemoremathguy View Post
    i need help finding the volume of a spherical cap. the only information i know is that the rim of the cap is 5m and its height is 2m.

    I have tried integrating using the formula for a sphere but the problem is I don't know the radius of the sphere from which the cap came and I can't figure out where to go from there. please help. thanks
    You don't need the radius; you can determine it from the information given. Using pythagorean theorem:

    r^2=(\frac{5}{2\pi})^2+(r-2)^2

    r=\frac{25}{16\pi^2}+1

    For the volume, I suggest cylindrical coordinates:

    V=4\int_0^{\frac{\pi}{2}}\int_{\frac{25}{16\pi^2}-1}^{\frac{25}{16\pi^2}+1}\int_0^{\frac{5}{2\pi}}r\  ;dr\;dz\;d\theta

    V=4\int_0^{\frac{\pi}{2}}\int_{\frac{25}{16\pi^2}-1}^{\frac{25}{16\pi^2}+1}[\frac{r^2}{2}]_0^{\frac{5}{2\pi}}dz\;d\theta

    V=4\int_0^{\frac{\pi}{2}}\int_{\frac{25}{16\pi^2}-1}^{\frac{25}{16\pi^2}+1}[\frac{25}{8\pi^2}]dz\;d\theta

    V=4\int_0^{\frac{\pi}{2}}[\frac{25}{4\pi^2}]d\theta

    V=\frac{25}{2\pi}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cylindrical and Spherical coords volume
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 7th 2011, 12:02 AM
  2. Calc 3- Volume using spherical coordinates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 12th 2010, 07:51 PM
  3. 3D volume problem with spherical coordinates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 6th 2009, 02:36 AM
  4. Volume of Spherical Cap Section
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 5th 2009, 08:39 AM
  5. Calculating the volume of a spherical cap.
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 27th 2008, 02:33 PM

Search Tags


/mathhelpforum @mathhelpforum