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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 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
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?
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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