Rate
Sand is falling off a conveyor onto a conical pile at the rate of 15 cubic feet per minute. The diameter of the base of the cone is appoximately twice thealtitude. At what rate is the height of the pile changing when it is 10 feet high?
Homework Answers
d = 2h
(so r = h)
dV/dt = 15ft³/min
Want:
dh/dt
V = p r² h /3
Sub r = h
V = p h³ /3
Differentiate with respect to time
dV/dt = p h² dh/dt
15 = p (10)² dh/dt
dh/dt = 15/100p
= 0.047746 ft/min (6dp)
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