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 solids rotating about two axises

  1. Apr 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the volumes of the solids revolution obtained by rotating the region about the x-axis and the y-axis.

    [itex]y=2x-x^2, y=0[/itex]



    3. The attempt at a solution
    I know how to get the volume of a function that is rotating around one axis, but the "y=0" is confusing me. Because [itex]y=2x-x^2[/itex] is a parabola (with a max at (1,1)), so when I picture it, it looks like a squished donut (with the hole having no area), where a cross sectional area of the donut is shaped like a football with the area being 4/3 (integral of [itex]f(x)=2x-x^2[/itex] from 0 to 2). The outer radius will be 2 and the inner radius will be 0.

    Is this correct, or am I completely off track? Also, what does the y=0 mean? Thanks
     
  2. jcsd
  3. Apr 2, 2012 #2

    Mark44

    Staff: Mentor

    y=0 is the lower boundary of the region.

    As I read it, this is actually two problems: 1) Find the volume when the region is revolved around the x-axis. 2) Find the volume when the region is revolved around the y-axis.
     
  4. Apr 2, 2012 #3

    Mark44

    Staff: Mentor

    Also, you should sketch each of the solids of revolution. When you revolve the region around the x-axis, you get something that looks a little like a football. When you revolve the region around the y-axis, you get something like the upper half of a bagel (what you described as a squished donut).

    For the two shapes, you'll need to choose what your typical volume element is - either a disk or a shell. In neither case is the outer radius fixed.
     
  5. Apr 2, 2012 #4
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook