Results 1 to 9 of 9

Math Help - bonus problem help

  1. #1
    Member
    Joined
    Feb 2010
    Posts
    98

    bonus problem help

    1. 1.[Bonus problem, show your work] Water is pumped into a inverted cone-shaped tank with the height 3 m and diameter 2m at the top. If the water level (h) is rising at a rate of 20cm/min in the tank, find out the rate of increasing for the water volume (V) in the tank when the water level is 1.5 m tall.


    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Black's Avatar
    Joined
    Nov 2009
    Posts
    105
    Given is

    \frac{dh}{dt}=20 \times 10^{-2} \, \text{m/min}.

    Your objective is to find

    \left. \frac{dV}{dt}\right|_{h=1.5}

    Volume of a cone w/ radius r and height h is

    V=\frac{1}{3}\pi r^2 h.

    You want to put V in terms of h alone then differentiate w/ respect to t. Using similarity of triangles you get the equation

    \frac{r}{h}=\frac{1}{3}.

    Solve for r, plug it in the volume equation, then differentiate w/ respect to t.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2010
    Posts
    98
    Quote Originally Posted by Black View Post
    Given is

    \frac{dh}{dt}=20 \times 10^{-2} \, \text{m/min}.

    Your objective is to find

    \left. \frac{dV}{dt}\right|_{h=1.5}

    Volume of a cone w/ radius r and height h is

    V=\frac{1}{3}\pi r^2 h.

    You want to put V in terms of h alone and differentiate w/ respect to t. Using similarity of triangles you get the equation

    \frac{r}{h}=\frac{1}{3}.

    Solve for r, plug it in the volume equation, then differentiate w/ respect to t.
    Ok thanks.. But I don't know how to do it when you say differentiate w/ respect to t
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Black's Avatar
    Joined
    Nov 2009
    Posts
    105
    Plugging r in the volume equation gives us

    V=\frac{1}{27}\pi h^3.

    Differentiating wrt t gives us

    \frac{dV}{dt}=\frac{1}{9}\pi h^2 \frac{dh}{dt}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2010
    Posts
    98
    ok so what do I do with the (1/9)(pi)(h^2)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member Black's Avatar
    Joined
    Nov 2009
    Posts
    105
    Plug in h = 1.5 m and dh/dt= .2 m/min into the equation to get your answer.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Feb 2010
    Posts
    98
    ok thanks
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Feb 2010
    Posts
    98
    so i should get (9pi/180) ??
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by tbenne3 View Post
    so i should get (9pi/180) ??
    Aren't bonus problems meant to be your own work ....?

    Thread closed. (pm me if I'm incorrect in the above assumption ....)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Investing her bonus
    Posted in the Algebra Forum
    Replies: 7
    Last Post: November 12th 2009, 11:31 AM
  2. Bonus Calculation
    Posted in the Algebra Forum
    Replies: 5
    Last Post: August 1st 2009, 09:36 AM
  3. bonus word problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 25th 2009, 05:57 PM
  4. Bonus...
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 17th 2009, 06:25 AM
  5. Replies: 1
    Last Post: May 29th 2007, 11:17 PM

Search Tags


/mathhelpforum @mathhelpforum