Results 1 to 2 of 2

Math Help - rate of change help

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    11

    rate of change help

    A rectangular prism`s length is is increasing by 12 meters per min, its height increasing by 2 meters per min and its width increasing by 4 meters per minute. How fast is the volume changing when the dimensions are:
    length = 200 m
    width = 50 m
    height = 30 m

    Can`t seem to figure this one out. Thanks for any help
    -Jackson
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,711
    Thanks
    630
    Hello, TheJacksonater!

    A rectangular prism`s length is increasing by 12 m/min,
    its height increasing by 2 m/min and its width increasing by 4 m/min.
    How fast is the volume changing when the dimensions are:
    length = 200 m, width = 50 m, height = 30 m.
    We are given: . \begin{Bmatrix}<br />
\dfrac{dL}{dt}&=&12 \\ \\[-3mm] \dfrac{dW}{dt} &=& 4 \\ \\[-3mm]<br />
\dfrac{dH}{dt} &=& 2 \end{Bmatrix} \quad\text{ and }\quad<br />
\begin{Bmatrix}L &=&200 \\ W &=&50 \\ H&=&30 \end{Bmatrix}


    We know that: . V \;=\:L\cdot W\cdot H

    Differentiate with respect to time: . \frac{dV}{dt} \;=\;L\!\cdot\!W\!\cdot\frac{dH}{dt} + L\!\cdot\!H\!\cdot\!\frac{dW}{dt} + W\!\cdot\!H\!\cdot\!\frac{dL}{dt}


    Therefore: . \frac{dV}{dt} \;=\;(200)(50)(2) + (200)(30)(4) + (50)(30)(12) \;=\;\boxed{62,000\text{ m}^3\text{/min}}


    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: April 12th 2011, 09:51 AM
  2. rate change
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 11th 2008, 03:11 AM
  3. rate of change
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 20th 2008, 07:53 AM
  4. rate of change
    Posted in the Calculus Forum
    Replies: 9
    Last Post: May 3rd 2007, 09:39 AM
  5. Rate of change
    Posted in the Statistics Forum
    Replies: 2
    Last Post: April 18th 2007, 07:27 AM

Search Tags


/mathhelpforum @mathhelpforum