Results 1 to 2 of 2

Math Help - Quick problem

  1. #1
    Junior Member
    Joined
    Sep 2007
    Posts
    56

    Quick problem

    There is a trough that is 7 feet long, and its vertical cross sections are inverted isosceles triangles with a height 5 feet and base 2 feet. There is water in it and and the water is being siphoned out at the rate of 3 cubic feet per minute. At any time t, let d be the depth and V be the volume of the water in the trough.

    1. Find the volume of the trough when its full.
    2. What is the rate of change in the area of the surface of the water at the instant when the trough is .25 full by volume?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    The area of the triangle formed by a cross section of the trough is

    \frac{1}{2}bh

    By similar triangles \frac{b}{h}=\frac{2}{5}

    b=\frac{2h}{5}

    The volume at some height h is then

    V=7\cdot\frac{1}{2}(\frac{2h}{5})h=\frac{7h^{2}}{5  }

    The full volume of the trough is V=\frac{1}{2}(2)(5)(7)=35

    Therefore, when it is 1/4 full by volume:

    \frac{35}{4}=\frac{7h^{2}}{5} and h=\frac{5}{2} and b=1

    Now, can you take it from there by differentiating and finding dh/dt.

    The surface area of the water at some height h would be given by the length of the trough times b (the width of the water surface at some height).

    S=7b=\frac{14h}{5}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quick Problem
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: February 23rd 2010, 10:31 AM
  2. Replies: 3
    Last Post: April 13th 2009, 06:42 PM
  3. One Quick Mean Value Problem!!!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 30th 2009, 06:53 PM
  4. Quick volume problem
    Posted in the Geometry Forum
    Replies: 4
    Last Post: February 23rd 2008, 12:31 PM
  5. Quick Problem.
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: October 22nd 2007, 02:16 PM

Search Tags


/mathhelpforum @mathhelpforum