High Height

May 25, 2010

High Height
How fast is the height of the pile increasing when the pile is 15 ft high?

Gravel is being dumped from a conveyor belt at a rate of 25 ft^3/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 15 ft high? Give your answer correct to three decimal places.

V = pi/3*r^2*h
d = h = 2r
V = 2pi/3*r^3
V'(r) = 2pi*r^2
25 = 2pi*r^2
r = 1.9947 ft/min
h = 3.9894 ft/min

the postal service - such great heights High Rez
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