Results 1 to 2 of 2

Math Help - Related rates of change

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    59

    Related rates of change

    The surface area of a cube is changing at the rate of 8 cm^2/s. How fast is the volume changing when the surface area is 60cm?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by scubasteve94 View Post
    The surface area of a cube is changing at the rate of 8 cm^2/s. How fast is the volume changing when the surface area is 60cm^2?
    Hi scubasteve94,

    if it is a regular cube, then

    surface\ area=6s^2

    volume=s^3

    where s=length of all edges

    SA=60\ cm^2=6s^2\ \Rightarrow\ s^2=10\ cm^2\ \Rightarrow\ s=\sqrt{10}\ cm

    \frac{d}{dt}(SA)=8\ cm^2/sec\ =\ \frac{ds}{dt}\ \frac{d}{ds}6s^2=\frac{ds}{dt}12s=\frac{ds}{dt}12\  sqrt{10}\ cm

    hence

    \frac{ds}{dt}=\frac{8}{12\sqrt{10}}=\frac{2}{3\sqr  t{10}}\ cm/sec..... which is the rate of change of the length of an edge of the cube.

    \frac{dV}{dt}=\frac{dV}{ds}\ \frac{ds}{dt}=3s^2\ \frac{2}{3\sqrt{10}}=30\ \frac{2}{3\sqrt{10}}=\frac{20}{\sqrt{10}}\ cm^3/sec
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Related Rates of Change
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 8th 2011, 03:26 AM
  2. Related rates of change.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 20th 2010, 01:17 PM
  3. related rates of change
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 5th 2009, 06:49 AM
  4. related rates of change
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 2nd 2009, 03:10 PM
  5. Related rates of change
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 8th 2008, 08:44 AM

Search Tags


/mathhelpforum @mathhelpforum