A shallow vessel for a chemical process is required in the form of an inverted cone, where the height h (in metres); is related to the radius 7 (in metres) by the formula, h = 1-r. You have been assigned the task of finding the dimensions of r and h which will maximise the capacity (V) of the vessel. (a) Show that V = πr² – ½ær³. (b) Determine the two values of r associated with the stationary points of V. (c) Why can we reject the lesser value for r without further consideration? (d) Show that the other value of r gives the maximum capacity of the vessel. (e) What should the value of h be to give the maximum capacity?
A shallow vessel for a chemical process is required in the form of an inverted cone, where the height h (in metres); is related to the radius 7 (in metres) by the formula, h = 1-r. You have been assigned the task of finding the dimensions of r and h which will maximise the capacity (V) of the vessel. (a) Show that V = πr² – ½ær³. (b) Determine the two values of r associated with the stationary points of V. (c) Why can we reject the lesser value for r without further consideration? (d) Show that the other value of r gives the maximum capacity of the vessel. (e) What should the value of h be to give the maximum capacity?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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![A shallow vessel for a chemical process is required in the form of
an inverted cone, where the height h (in metres); is related to the
radius r (in metres) by the formula, h = 1 - r. You have been
assigned the task of finding the dimensions of r and h which will
maximise the capacity (V) of the vessel.
Th
(a) Show that V = πr² – ²7ar³.
(b) Determine the two values of r associated with the stationary points of V.
(c) Why can we reject the lesser value for r without further consideration?
(d) Show that the other value of r gives the maximum capacity of the vessel.
(e) What should the value of h be to give the maximum capacity?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd000f3ec-5744-44d4-a2b8-3b46a02ad4a6%2Fc4bac8c7-cde3-432f-973f-0a61421b46c4%2Feiduoi4_processed.gif&w=3840&q=75)
Transcribed Image Text:A shallow vessel for a chemical process is required in the form of
an inverted cone, where the height h (in metres); is related to the
radius r (in metres) by the formula, h = 1 - r. You have been
assigned the task of finding the dimensions of r and h which will
maximise the capacity (V) of the vessel.
Th
(a) Show that V = πr² – ²7ar³.
(b) Determine the two values of r associated with the stationary points of V.
(c) Why can we reject the lesser value for r without further consideration?
(d) Show that the other value of r gives the maximum capacity of the vessel.
(e) What should the value of h be to give the maximum capacity?
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