Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spherical Section Volume

  1. Dec 14, 2004 #1
    How do I find the volume of a bowl shaped section of a sphere, given the depth of the section. I know i can integrate it, but a friend says that i can find the volume of a cone with equal height and radius, and then use that to find the volume of the spherical section.
  2. jcsd
  3. Dec 14, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    Find the volume of the sector of the sphere that includes the bowl and subtract from it that volume of a cone whose vertex is at the center of the cone and whose base is the (flat) top of the bowl.
  4. Dec 14, 2004 #3
    Thanks Tide, but the equation for the sector of a sphere is derived using calculus. Is there any way to find the equation for the spherical cap without calculus? And by calculus, i mean integration.
  5. Dec 14, 2004 #4


    User Avatar
    Science Advisor
    Homework Helper

    I don't know if there is a way to do it without calculus but I think the point is that it is a lot easier to find the desired volume using the sector and cone approach than it is to integrate directly. If someone is clever enough to get it without calculus I'd love to see it!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Spherical Section Volume
  1. Conic Sections (Replies: 5)

  2. Conic sections (Replies: 9)

  3. Conic sections (Replies: 4)