1. Limited time only! Sign up for a free 30min personal 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 the solid using a cylindrical cross section

  1. Aug 1, 2012 #1
    [STRIKE][/STRIKE]1. The problem statement, all variables and given/known data
    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.


    2. Relevant equations

    [itex]y = \sqrt{x-1} , y = 0, x = 5;[/itex] about [itex]y = 3[/itex]


    3. The attempt at a solution
    I already completed graphing it, but not really sure how to show that here.

    2[itex]\pi[/itex][itex]\int_0^2[/itex](shell radius)(shell height) [itex]dy[/itex]
    2[itex]\pi[/itex][itex]\int_0^2[/itex][itex](y)(y^2+1)[/itex] [itex]dy[/itex]
    2[itex]\pi[/itex][itex]\int_0^2[/itex][itex](y^3+y)[/itex] [itex]dy[/itex]
    [itex]2\pi (((y^4)\div4)) + (y^2)\div2)[/itex]
    [itex]2\pi(4+2) - 0[/itex]
    [itex]12\pi[/itex]

    Is that correct? I'm not sure if I did the shell height correctly.
     
  2. jcsd
  3. Aug 1, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You are rotating around y= 3 which means that the axis of each cylinder is y= 3 and the radius is 3- y, not y.
     
  4. Aug 1, 2012 #3
    Aha, thank you so much! :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Volume of the solid using a cylindrical cross section
Loading...