Results 1 to 3 of 3

Math Help - variant conical glass problem

  1. #1
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448

    variant conical glass problem

    A conical glass of depth h and generating angle A, there is carefully dropped spherical iron ball of such size as to cause the greatest overflow. What is the generating angle A that will cause the greates overflow.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by pacman View Post
    A conical glass of depth h and generating angle A, there is carefully dropped spherical iron ball of such size as to cause the greatest overflow. What is the generating angle A that will cause the greatest overflow.
    There is no upper bound to the amount of overflow. Imagine a glass with generating angle very close to 90°. In order to have depth h, it will have to be immensely wide and therefore have an enormous capacity. If a huge ball is (very carefully) lowered into it, the amount of liquid displaced can be arbitrarily large.

    If you want a more mathematical argument, notice that the critical value for x found in the previous thread has a denominator which goes to 0 as A approaches 90°. You can check that the same denominator occurs in the expression for the greatest overflow.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    Thanks opalg, your analysis of the problem is very clear to me, but i am thinking along the line when the ball is totally submerged, barely enough touching the surface of the liquid. That one bothers me . . . ..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. a variant of Ricci curvature
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 11th 2011, 02:26 PM
  2. conical glass
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 30th 2009, 03:12 AM
  3. Conical paper cup - Work problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 28th 2009, 04:58 PM
  4. Einstein Riddle Variant
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: October 20th 2008, 07:02 AM

Search Tags


/mathhelpforum @mathhelpforum