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!

Find the volume of the solid obtained by rotating the region

  1. Jan 21, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
    y = 5x, y = 5[itex]\sqrt{x}[/itex] about y = 5

    2. Relevant equations
    A(x)=∏(R2-r2)

    3. The attempt at a solution
    A(x)=∏(5x)2-(5[itex]\sqrt{x}[/itex])2)
    A(x)=∏(25 x2 - [itex]\frac{10}{3}[/itex]x[itex]\frac{3}{2}[/itex])

    V=∏[itex]\int[/itex][itex]^{1}_{0}[/itex](25x2- [itex]\frac{10}{3}[/itex]x[itex]\frac{3}{2}[/itex])dx

    V=∏([itex]\frac{25}{3}[/itex]x3-[itex]\frac{4}{3}[/itex]x[itex]\frac{5}{2}[/itex]) {0,1}

    V=∏([itex]\frac{25}{3}[/itex]-[itex]\frac{4}{3}[/itex])
    V= [itex]\frac{21}{3}[/itex]∏

    Where did I go wrong? I can't figure out the about y=5. If I am correct, you would usually subtract 5 from the two radii, but since they intersect at y=5, the just flip on that intersection point and thus we don't need to find the lost area. Bad explanation, I know, maybe someone can explain it to me.

    Thanks in advance!
     
  2. jcsd
  3. Jan 21, 2012 #2

    Mark44

    Staff: Mentor

    You've made an error right off the bat. I hope you sketched the region being rotated.

    You aren't taking into account the fact that the axis of rotation is the line y = 5. The larger radius, R, is 5 - 5x. The smaller radius, r, is 5 - 5√x.

    Also, your relevant equation is missing a factor - Δx. If you substitute the values above for R and r, you should get the right result.
     
  4. Jan 21, 2012 #3
    Ok, that's what my question at the end was about. I wasn't sure if I was supposed to subtract the radii from 5. I'll try it out and see how it goes. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook