SOLUTION: Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are alway

Question 1127031: Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 5 ft high? (Round your answer to two decimal places.)
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.

The volume of a cone   V = .


Since we are given that  h = 2r (where 2r is the diameter), 


    V =  =  = .    (1)


The rate of the volume change in time is given;  it is 15 ;  therefore


15 =  =  = (calculate  from the formula (1)) = . = (substitute here h= 5 ft) = ..


It implies   =  =  =  = 0.76 ft/min.  (rounded)


Answer.  At this moment, the height of the cone is increasing at the rate of  0.76 ft/min. (approximately)

Solved.

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