Results 1 to 2 of 2

Math Help - Help with application: 'Cylinder filling with water, rate of sqrt(x), derive formula'

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    16

    Help with application: 'Cylinder filling with water, rate of sqrt(x), derive formula'

    Hey guys, I'm completley stuck on question 2)a)i).

    Everything I do leads me in a circle, of either the x's cancelling, or me getting no where. Can anyone direct me the right way, how should I set up the problem? Thanks.

    Here's the question, I need help on Q2)a)i):
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello Phatmat
    Quote Originally Posted by Phatmat View Post
    Hey guys, I'm completley stuck on question 2)a)i).

    Everything I do leads me in a circle, of either the x's cancelling, or me getting no where. Can anyone direct me the right way, how should I set up the problem? Thanks.

    Here's the question, I need help on Q2)a)i):
    When the depth of water is x metres, suppose that the volume of water is V \text{m}^3. Then if the time t is measured in minutes, the rate of increase of V with respect to t is \frac{dV}{dt} \text{m}^3/\text{min}. This is the rate at which water is filling the tank.

    So \frac{dV}{dt}=\sqrt x

    The volume of a cylinder = \pi r^2 h. So when r = 2 and h = x, V = 4\pi x

    \Rightarrow \frac{dV}{dx}=4\pi

    \Rightarrow \frac{dV}{dt}=\frac{dV}{dx}\cdot\frac{dx}{dt}=4\pi  \frac{dx}{dt}

    \Rightarrow 4\pi\frac{dx}{dt}=\sqrt x

    Can you continue from here?

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: March 9th 2012, 09:08 AM
  2. Application! Sprinklers and water speed.
    Posted in the Calculus Forum
    Replies: 11
    Last Post: September 26th 2011, 02:20 PM
  3. rate of flowing water
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 30th 2010, 02:05 PM
  4. calculate water depth rate..
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 19th 2009, 09:26 AM
  5. cylinder with water
    Posted in the Geometry Forum
    Replies: 5
    Last Post: August 7th 2007, 07:40 AM

Search Tags


/mathhelpforum @mathhelpforum