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!

Volumes of Revolution Question

  1. Dec 11, 2014 #1

    RJLiberator

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Let R be the region bounded by the curves y=0 and y=x^2+x between x=0 and x=1. Compute the volume of the solid of revolution obtained when R is rotated about the axis y=-1.

    2. Relevant equations
    Disc method: integral of pi*r^2 = volume from the bounds

    3. The attempt at a solution

    The bounds are obvious = 0 to 1.

    The hard part is accounting for the empty area inbetween as we rotate around y=-1 rather then y=0.

    What I did to solve the problem was moved the volume up 1 to the origin. I then solved the entire volume of the problem from 0 to 1 using the radius of x^2+x+1 (the +1 to account the entire area).
    My answer here was 37pi/10.

    I then went back and took the volume of the squared middle region which had radius of 1 and then subtracted that from my first answer.

    My final answer was 27pi/10.

    Can anyone confirm my train of thought/answer?

    Thank you.
     
  2. jcsd
  3. Dec 11, 2014 #2

    Mark44

    Staff: Mentor

    That works for me.

    You could also do the problem without translating the region upward like so:
    ##\Delta V = \pi[(\text{outer radius})^2 - (\text{inner radius})^2]\Delta x##
    where the outer radius is ##x^2 + x - (-1) = x^2 + x + 1## and the inner radius is 1.
    The volume integral is then
    ##\pi \int_0^1 [(x^2 + x + 1)^2 - 1^2] dx##
     
  4. Dec 11, 2014 #3

    RJLiberator

    User Avatar
    Gold Member

    Ah, so you managed to get the same answer as well? Confirming my result :D
     
  5. Dec 12, 2014 #4

    Mark44

    Staff: Mentor

    Yes, same answer.
     
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: Volumes of Revolution Question
Loading...