Results 1 to 2 of 2

Math Help - Find the area of a cone inside a cylinder

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    5

    Unhappy Find the area of a cone inside a cylinder

    Hi! I'm trying to find the area of the cone x^2+y^2=z^2 inside x^2+(y-a)^2=a^2 -- but I believe I'm stuck... :/
    I parametrize the cone as r=u*i+v*j+sqrt(u^2+v^2)k, find dr/du=i+u/sqrt(u^2+v^2)*k and dr/dv=j+v/sqrt(u^2+v^2)k, then the cross product dr/du*dr/dv=-u/sqrt(u^2+v^2)*i-v/sqrt(u^2+v^2)*j +k and the area element dS=norm(dr/du*dr/dv)du*dv=sqrt(2)*du*dv.
    How shall I proceed now? I simply can't think of any good way...

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Oct 2009
    Posts
    5

    Re: Find the area of a cone inside a cylinder

    Ok, I just found out, I wrote it on polar form and integrated 0≤theta≤pi/2, 0≤r≤2a*sin(theta) 4*integral(r*dr*dtheta), and the answer is s*sqrt(2)*a^2*pi.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Surface of the cone inside the cylinder
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 27th 2010, 05:21 AM
  2. Area of a surface inside a cylinder
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 26th 2010, 04:05 PM
  3. Surface area of cone lying inside a cylinder
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 24th 2010, 10:25 AM
  4. how to find maximum volume of cube inside cone
    Posted in the Calculus Forum
    Replies: 8
    Last Post: June 14th 2009, 12:07 AM
  5. Fitting a cylinder inside a cone
    Posted in the Geometry Forum
    Replies: 3
    Last Post: March 19th 2009, 02:37 PM

Search Tags


/mathhelpforum @mathhelpforum