1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Chain rule homework

  1. Sep 27, 2004 #1
    Does anyone know how to do this with chain rule??? :surprised

    If a cone has height 1 m and radius 30 cm, and the height is increasing at a rate of 1 cm/s, whereas the radius is decreasing at a rate of 1 cm/s, what is the rate of change of the cones volume? Solve the problem using the chain rule.

  2. jcsd
  3. Sep 27, 2004 #2
    dr/dt = .1 r = .1t + .3
    dh/dt = .1 h= .1t + 1

    v = 1/3 pi r^2 h
    v = 1/3 pi (.1t+.3)^2 (.1t +1)
    dv/dt = 1/3 pi 2(.1t+3) (.1) (.1)
    notice chain rule used

    dv/dt = 2pi/3 (.001t + .003)
  4. Sep 28, 2004 #3


    User Avatar
    Science Advisor

    Or: Since [itex] V= \frac{\pi}{3}r^h[/itex], [itex]\frac{dV}{dt}= \frac{2\pi}{3}rh\frac{dr}{dt}+ \frac{\pi}{3}r^2[/itex]
    (both product rule and chain rule used!)
    We are told that [itex]\frac{dr}{dt}= -1 cm/sec [/itex] and [itex]\frac{dh}{dt}= 1 cm/sec[/itex]
    (Phymath: you missed the fact that r is decreasing! Also you do not state the units, which is crucial.)
    so [itex]\frac{dV}{dt}=\frac{\pi}{3}r^2- \frac{2\pi}{3}rh cm^3/sec[/itex]
    Last edited by a moderator: Sep 28, 2004
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook