Results 1 to 5 of 5

Math Help - A geometry/derivative word problem

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    7

    A geometry/derivative word problem

    a container has the shape of an open right circular cone, as shown in the figure above. The height of the container is 10 cm and the diameter of the opening is 10 cm. Water in the container is evaporating so that it depth h is changing at the constant rate of -3/10 cm/hr.
    The volume of a cone of height h and radius r is given by V=1/3 pi r^2 h
    a) Find the volume V of water in the container when h=5 cm.
    b) find the rate of change of volume of water in the container, with respect to time, when h=5 cm.
    I know you suppose to find an equation and take the derivative, but how to do it i don't know.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2008
    Posts
    18
    1)V=1/3 pi r^2 h

    ookay. the cone has a radius of 10 and a height of 10. in order to find the radius when the height is 5, we need a proportion.
    10/10 = 5/r
    we can conclude r=5 cm as well, and we can solve for Volume!!

    2)dV/dt can be found by differentiating the equation for volume..

    it was given that dh/dt=-3/10.

    using a proportion similiar to the one above, we know
    10/10=h/r
    therefore h=r

    we can eliminate r in the volume equation by plugging in h:
    V=1/3 Pi r^2 h r=h
    V=1/3 Pi h^3

    differentiate that:
    dV/dt = 1/3 Pi 3h^2 * dh/dt
    solve!
    Last edited by sarabolha; November 28th 2008 at 09:16 PM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jun 2009
    Posts
    82

    Re: A geometry/derivative word problem

    The diameter is 10. The radius is 5 cm.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,120
    Thanks
    805

    Re: A geometry/derivative word problem

    think he probably either graduated or failed out by now....
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jun 2009
    Posts
    82

    Re: A geometry/derivative word problem

    Sure, but other people may look at the answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Geometry Word Problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: June 6th 2009, 07:03 AM
  2. [SOLVED] Word Geometry Problem
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 18th 2009, 11:27 AM
  3. Replies: 2
    Last Post: January 10th 2009, 05:49 AM
  4. Geometry Word Problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 2nd 2007, 08:24 AM
  5. Geometry - word problem
    Posted in the Geometry Forum
    Replies: 14
    Last Post: January 13th 2006, 12:40 PM

Search Tags


/mathhelpforum @mathhelpforum