Results 1 to 3 of 3

Math Help - Cylindrical Shells

  1. #1
    Junior Member winterwyrm's Avatar
    Joined
    Oct 2007
    Posts
    67

    Cylindrical Shells

    Ok, got another one for you, thanks for all the help, you guys are great!

    If the base of a solid is given by the ellipse: (x^2)/4 + (y^2)/9 = 1
    then what is it's volume if the solid (cross sectional view) is an isosceles triangle of heigt 2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by winterwyrm View Post
    Ok, got another one for you, thanks for all the help, you guys are great!

    If the base of a solid is given by the ellipse: (x^2)/4 + (y^2)/9 = 1
    then what is it's volume if the solid (cross sectional view) is an isosceles triangle of heigt 2?
    Refer back to my previous post here.

    Just note that the area of the slices will change:

    Area_{\triangle}=\tfrac{1}{2}(base)(height)=\tfrac  {1}{2}\left[\tfrac{4}{3}\sqrt{9-x^2}\right](2)=\tfrac{4}{3}\sqrt{9-x^2}

    Thus, V(x)=\tfrac{8}{3}\int_0^3 \sqrt{9-x^2}\,dx

    Take note of this: To evaluate the integral...make a trig substutition:

    let x=3\sin\vartheta.

    Can you take it from here?

    --Chris

    EDIT : Woops...I just noticed that the equation changed slightly...

    the distance from one side of the ellipse to the other should now be 3\sqrt{4-x^2} (Verify)

    Thus, the area of each slice would be 3\sqrt{4-x^2} and the volume would be 6\int_0^2 \sqrt{4-x^2}\,dx

    You still would need to apply a trig substitution:

    let x=2\sin\vartheta
    Last edited by Chris L T521; August 2nd 2008 at 01:12 PM. Reason: wrong limit of integration...>_>
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member winterwyrm's Avatar
    Joined
    Oct 2007
    Posts
    67
    Thanks, I just got a little bit confused with the trig, wow, I didn't even notice they swapped it up on me. I guess I need to review my integration...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with cylindrical shells
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 18th 2011, 04:20 AM
  2. cylindrical shells
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 8th 2010, 02:40 PM
  3. using cylindrical shells
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 5th 2010, 04:38 AM
  4. use cylindrical shells...
    Posted in the Calculus Forum
    Replies: 7
    Last Post: March 29th 2010, 04:45 AM
  5. Cylindrical shells:
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 24th 2007, 12:21 PM

Search Tags


/mathhelpforum @mathhelpforum