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: Related Rates Sand Pile Problem

  1. Jan 11, 2016 #1
    1. The problem statement, all variables and given/known data
    A machine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. The height of the pile is always twice the length of the base diameter. After 5 minutes, how fast is the height increasing? After 5 minutes, how fast is the area of the base increasing?

    2. Relevant equations

    V = (1/3)(pi)r^2(h)

    3. The attempt at a solution

    For the first question,
    ##h = 4r##
    ##\displaystyle V(t) = 20t = \frac{1}{3}\pi r^2 h = \frac{\pi}{48}h^3##
    From this equation I get
    ##\displaystyle h = (\frac{960}{\pi}t)^{\frac{1}{3}}##
    ##\frac{dh}{dt} = \frac{320}{\pi ((\frac{960}{\pi})t)^{\frac{2}{3}}}##
    When 5 is substituted for t, I get 0.77 m^3/min. Is this correct?

    Also, I am not sure how to approach the second problem. I know that the area of the base is ##\pi r^2##, but I am not sure how to proceed...
    Last edited: Jan 11, 2016
  2. jcsd
  3. Jan 11, 2016 #2
    Use the fact that height is equal to twice the diameter of the base at all times.
    Last edited: Jan 11, 2016
  4. Jan 11, 2016 #3
    I did that for the first problem. I don't see how it will work for the second problem though.
  5. Jan 11, 2016 #4
    EDIT: ah never mind, fairly straightforward problem. Haven't seen one like this in awhile though.

    Method 1: If you're know what dH/dt is, try applying that to see what the radius would be.

    EDIT: you did the first part right.
    Suggested Hint: Try rewriting the area equation.

    ...and check your units to part 1.
    Last edited: Jan 11, 2016
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted