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. How fast is the height of the pile increasing when the pile is 18 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is -xrh given by V = 3 ft min

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 42AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
Question
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. How fast is the height of the pile increasing when the pile is 18 feet high?
Recall that the volume of a right circular cone with height h and radius of the base r is
1
-πr²h
3
given by V
=
ft
min
Transcribed Image Text: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. How fast is the height of the pile increasing when the pile is 18 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is 1 -πr²h 3 given by V = ft min
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