Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Surface area obtained by solid of revolution

  1. Mar 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Find surface area of solid of revolution obtained by rotating the curve:


    from x=5 to x=7, rotated about x=-4

    3. The attempt at a solution

    The problem is I know how to do this if I rotated it about x-axis/y-axis, but I have no idea how to do it if the axis is shifted. I did it pretending it was rotated about the y-axis (since x=-4 is parallel to the y-axis), and my answer came out wrong.

    I used:

    SA=∫2∏x ds, where ds=√(1+[f'(x)]2) dx

    So I found the derivative of the function, everything was fine. I squared and square-rooted, found the integral to be:

    ∏/10 ∫ x^2+100 dx (evaluated from 5 to 7)

    but i didn't use the piece of information "axis of rotation is x=-4" anywhere in my solution. I don't really know how to go about using it, please help?
  2. jcsd
  3. Mar 3, 2012 #2
    Do I just change the formula from SA=∫2∏x ds to SA=∫2∏(x+4) ds since the axis is shifted to the left 4 units, so the distance to the axis of rotation would be 4 units longer?

    Although the answer is still not correct...

    or do I change the function so that it goes from y=x^2/40-5lnx to y=(x-4)^2/40-5ln(x-4)? Or none of the above?:/
    Last edited: Mar 3, 2012
  4. Mar 3, 2012 #3
    Last edited: Mar 3, 2012
  5. Mar 3, 2012 #4
    Thanks for answering, but I don't understand the second part of the integral. Why is it (x^2/40-5lnx) dx?

    I thought it should be:

    ∫2∏(x+4) ds

    where ds is

    √(1+[f'(x)]^2) dx, and f'(x) is the derivative of x^2/40-5lnx?
  6. Mar 3, 2012 #5
    Last edited: Mar 3, 2012
  7. Mar 3, 2012 #6
    OHHH NEVERMIND! I'm stupid, you're looking for surface area, not volume. Ignore everything I've said, sorry!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook