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 rotated graph

  1. Mar 24, 2006 #1
    Hi. There are a few problems on my homework that involved the volume of a rotated solid. I do not know how to do these, but I'm trying to devise a method. This is what I figure:

    [tex]\int_{a}^{b} f(x) dx[/tex] is the area under the graph.

    [tex]\frac {\int_{a}^{b} f(x) dx} {b-a}[/tex] is the average height.
    This is where logic comes in:
    I figure you can use the mean value (average height) as the radius of an "average cylinder" of the function. Therefore, the volume would be [tex]\pi r^{2} (b-a)[/tex], where [tex]r[/tex] is [tex]\frac {\int_{a}^{b} f(x) dx} {b-a}[/tex].

    Is this correct? I will simplify once i confirm my Latex is correct.

    Alright, with this, is it okay to conclude that the over volume is [tex]V = \frac {\pi (\int_{a}^{b} f(x) dx)^2} {b-a}[/tex]?

    On a sidenote, I make mistakes quite often with Latex, is there an offline generator to check my syntax with?
     
    Last edited: Mar 24, 2006
  2. jcsd
  3. Mar 24, 2006 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Do you mean a volume of revolution? It looks like it.

    Not that I know of, but you do have 24 hours to edit your posts.
     
  4. Mar 24, 2006 #3

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    No. Consider a sphere of radius 1, centered at the origin, so r as you've defined it would be [itex]\pi /4[/itex], since the area under f will just be the area of half of a circle of radius 1, which is [itex]\pi /2[/itex], and then you divide by b-a = 1-(-1) = 2 to get r. So

    [tex]\pi r^2(b-a) = \pi ^3/8[/tex]

    On the other hand, you know the volume is [itex]4\pi /3[/itex].
     
  5. Mar 25, 2006 #4
    Mind helping me figure out how you actually do this then?
     
  6. Mar 25, 2006 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    If you used the distance from the axis of rotation to the centroid of the figure instead of the "average radius" then you would have Pappus' theorem.
    Here's a reference on volumes of revolution:
    http://www.maths.abdn.ac.uk/~igc/tch/ma1002/int/node22.html
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Volume of rotated graph
  1. Volume of Rotation (Replies: 5)

  2. Volume of rotation (Replies: 4)

  3. Volume of Rotation (Replies: 2)

  4. Volume of Rotation (Replies: 13)

Loading...