Results 1 to 4 of 4

Math Help - Rate of Change 2

  1. #1
    Junior Member
    Joined
    Sep 2008
    From
    Australia
    Posts
    72

    Rate of Change 2

    A metel sphere is dissolving in acid. It remains spherical and the rate at which its volume decreases is proportional to its surface area. Show that its radius is decreasing at a constant rate.

    What information and chain rules that can get from this question?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by sanikui View Post
    A metel sphere is dissolving in acid. It remains spherical and the rate at which its volume decreases is proportional to its surface area. Show that its radius is decreasing at a constant rate.

    What information and chain rules that can get from this question?
    \frac{dr}{dt} = \frac{dr}{dV} \cdot \frac{dV}{dt}.

    Given: \frac{dV}{dt} = k A = 4 k \pi r^2.

    Geometry: V = \frac{4}{3} \pi r^3 \Rightarrow \frac{dV}{dr} = \, ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    From
    Australia
    Posts
    72
    Quote Originally Posted by mr fantastic View Post
    \frac{dr}{dt} = \frac{dr}{dV} \cdot \frac{dV}{dt}.

    Given: \frac{dV}{dt} = k A = 4 k \pi r^2.

    Geometry: V = \frac{4}{3} \pi r^3 \Rightarrow \frac{dV}{dr} = \, ....
    Area of sphere: A =4 pi r^2.
    Let \frac{dV}{dt} = k A = 4 k \pi r^2. ( So, that: \frac{dV}{dt} = k A = 4 k \pi r^2. need to diff?)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,569
    Thanks
    1410
    Quote Originally Posted by sanikui View Post
    Area of sphere: A =4 pi r^2.
    Let \frac{dV}{dt} = k A = 4 k \pi r^2. ( So, that: \frac{dV}{dt} = k A = 4 k \pi r^2. need to diff?)
    The problem was to "Show that its radius is decreasing at a constant rate." In order to show that, you have to look at dr/dt.
    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