Homework Help Forum: calculus

Posted by Ash on Thursday, October 29, 2009 at 6:54pm.

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile increasing when the pile is 20 feet high?

• calculus - webwork problem?, Thursday, October 29, 2009 at 11:21pm

  v=1/3*pi*r^2h r=2/h V=1/3*pi*(h/2)^2*h =1/3*pi*h^2/4*h =1/12*pi*h^3 V'=10ft^3/min h=20ft V'=1/12*pi*3h^2*h' 10=1/12*pi*3(20)^2*h' solve for h'

  
  

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