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.8.ft.high? (Round your answer to two decimal places.) ft/min Enter a number. Enhanced Feedback Please try again. Keep in mind that the volume of the cone is given by V = ²h. You are told that 2r = h and П dv = dt (rate gravel is pumped in). Write the volume in terms of h only and differentiate the formula on both sides with respect to t using the Chain Rule. Now, using the given values, you can solve for the value of dh dt
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.8.ft.high? (Round your answer to two decimal places.) ft/min Enter a number. Enhanced Feedback Please try again. Keep in mind that the volume of the cone is given by V = ²h. You are told that 2r = h and П dv = dt (rate gravel is pumped in). Write the volume in terms of h only and differentiate the formula on both sides with respect to t using the Chain Rule. Now, using the given values, you can solve for the value of dh dt
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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.8.ft.high? (Round your answer to two decimal places.)
ft/min
Enter a number.
Enhanced Feedback
Please try again. Keep in mind that the volume of the cone is given by V = r²h. You are told that 2r= h and
T
dv
dt
(rate gravel is pumped in). Write the volume in terms of h only and differentiate the formula on both sides with
respect to t using the Chain Rule. Now, using the given values, you can solve for the value of
dh
dt
=
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