Results 1 to 4 of 4

Math Help - fun volume problem

  1. #1
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1

    fun volume problem

    Here is a cool volume problem if anyone would like a go.

    A cylindrical barrel of diameter d lies on a stand so that its axis makes an angle of 20 degrees with the horizontal. The amount of fluid in the barrel just covers the bottom of the barrel. Approximate the volume of fluid in the barrel
    Last edited by galactus; November 24th 2008 at 05:38 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    643
    Hello, galactus!

    A cylindrical barrel of diameter d lies on a stand
    so that its axis makes an angle of 20 with the horizontal.
    The amount of fluid in the barrel just covers the bottom of the barrel.
    Approximate the volume of fluid in the barrel.
    Code:
                                              D
                                              *
                                        *      *
                           L      *             * d
                            *                    *
                      *                           *
                *                                  *
         A* - - - - - - - - - - - - - - - - - - - - *C
          :*::::::::::::::::::::::::::::::::::*     :
          : *:::::::::::::::::::::::::::*           :
          :  *d:::::::::::::::::::* L               :
          :20*:::::::::::::*                       :
          :    *::::::*  20                        :
         P+ - - * - - - - - - - - - - - - - - - - - +Q
                B
    Let L = length of the cylinder.

    In \Delta APB\!:\;\;AP \:=\:d\cos20^o

    In \Delta CQB\!:\;\;CQ \:=\:L\sin20^O

    Since CQ = AP,\;\;L\sin20^o \:=\:d\cos20^o \quad\Rightarrow\quad L \;=\;d\cot20^o


    The fluid occupies half the volume of the cylinder: . V \;=\;\frac{1}{2}\cdot\pi\left(\frac{d}{2}\right)^2 L

    Therefore: . V \;=\;\frac{1}{2}\cdot\pi\cdot\frac{d^2}{4}(d\cot20  ^o) \;=\;\frac{\pi}{8}d^3\cot20^o

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Didn't take you long, Soroban. Good man. That's what I got. It wasn't particularly difficult, just a cool problem.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member pflo's Avatar
    Joined
    Apr 2009
    From
    Albuquerque, NM
    Posts
    155
    Thanks
    7
    This problem is relatively easy using geometry and trig. Can you do it by integrating (using calculus)?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to set this volume problem?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2009, 04:56 PM
  2. Replies: 2
    Last Post: January 10th 2009, 05:49 AM
  3. Volume problem...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: August 30th 2007, 05:51 PM
  4. Volume problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 10th 2007, 11:28 PM
  5. A volume/SA problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 2nd 2006, 12:29 PM

Search Tags


/mathhelpforum @mathhelpforum