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 a Region inside a cylinder and sphere (Symbolic)

  1. Nov 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Suppose W is the region inside the cylinder x^2+y^2=a^2 and inside the sphere x^2+y^2+z^2=b^2, where 0<a<b.
    Set up an iterated integral for the volume of W

    2. Relevant equations
    x^2+y^2+z^2=b^2
    x^2+y^2=a^2
    0<a<b
    3. The attempt at a solution
    I converted to cylindrical coordinates and tried to set up the triple integral as follows
    [rdzdthetadr], where -sqrt(b^2-r^2)<=z<=sqrt(b^2-r^2), 0<=theta<=2pi, 0<=r<=a. Am I at least on the right track for the integral? Any help is seriously appreciated. Thank you! :)
    P.S. (<= is meant to be 'less than or equal to'), just figured I'd clarify :)
     
  2. jcsd
  3. Nov 15, 2016 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That looks correct.
     
  4. Nov 16, 2016 #3
    Thank you for the reply. I spend way longer than I should have on this problem. I thought it was more complicated than this, so I am happy that the solution was easier than expected. Cheers! :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Volume of a Region inside a cylinder and sphere (Symbolic)
  1. Sphere-Cylinder Volume (Replies: 6)

Loading...