1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Volumn by cross sections - solving in terms of which axis confusion?

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data

    I need to find the volume of the solid generated by revolving this region bounded by the curves about the x-axis.

    y = sqrt(x), x+y=6, y=1

    2. Relevant equations

    3. The attempt at a solution

    I find the intersections of these curves I get:

    (1,1), (4,2), (5,1)..
    Then I see that to get the area of this cross section I need to do two sections from x = 1 to x = 4, and x = 4 to x = 5 if I integrated in terms of x..

    So I see that it will be easier to integrate in terms of y:

    I will get the area to be

    A(y) = \int_{1}^{2} [(-y+6)-(y^2)]dy

    But now I am confused as to how I can formulate the integral to find the volume of this by revolving around the x-axis?

    I know I need to use the difference of the boundary as the radius then multiply by pi.. but I don't understand how to do that if I wrote the area in terms of y?
  2. jcsd
  3. Feb 3, 2010 #2


    Staff: Mentor

    Forget the integral you have. That just gives you the area of the region, which isn't what you want.

    Your typical volume element is a shell whose volume is 2* pi*radius*length*[itex]\Delta y[/itex]. For your problem radius is y, and length is (6 - y - y2). The limits of integration are the ones you found, y = 1 and y = 2.

    BTW, you should have put this into the Calculus and Beyond section, not the Precalcus section.
  4. Feb 3, 2010 #3
    So can I do this to find the volume?


    V = \int_{1}^{2} \pi[(-y+6)^2-(y^2)^2]dy

  5. Feb 3, 2010 #4


    Staff: Mentor

    Reread what I wrote in post #2.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Volumn cross sections Date
Probability of getting an ace in case of a loaded die Nov 21, 2017
Vector cross product Sep 28, 2016
Double cross product Sep 22, 2015
Proving volume of box using cross and dot product Sep 8, 2015
Vector cross product Apr 8, 2015