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!

Consider the circle D on the plane with the center (2,0) and radius r=1. Revolving D

  1. Dec 18, 2008 #1
    1. The problem statement, all variables and given/known data

    Consider the circle D on the plane with the center (2,0) and radius r=1. Revolving D about the y-axis, we obtain a donut (torus). What is the volume of this donut?

    2. Relevant equations

    Assume: [tex]
    F(x)=\int^{a}_{-a} sqrt(a^2-u^2)du[/tex] = (PI * a^2 )/2 where a[tex]\geq0[/tex]


    3. The attempt at a solution

    I sincerely apologize, I have no idea as to where to even get started.
     
  2. jcsd
  3. Dec 18, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Consider the circle D on the plane with the center (2,0) and radius r=1. Revolvin

    Can we at least assume you are taking a Calculus class and that you are dealling with "volumes of rotation" right now? You can do this by using "washers" or "cylinders".
    In either case, the first thing you should do is draw a picture- graph the circle.

    Washers: Draw a horizontal line across the circle at a fixed "y" value and imagine that being rotated around the y-axis. It forms a "washer"- the region between two circles. Its area is the difference between the areas of those two circles. If you think of it as having height "dy" then its volume is that area times dy. Integrate from the lowest y value in the circle to the highest.

    Cylinders: Draw a vertical line through the circle at a specific x and imagine it rotated around the y-axis so that it forms a cylinder. Its surface area is the circumference of the circle, [itex]2\pi x[/itex], times the length of that line. If you think of it has having thickness dx, its volume is that area times dx and the volume of the whole thing is the integral of that from the lowest x value in the circle to the highest.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Consider the circle D on the plane with the center (2,0) and radius r=1. Revolving D
Loading...