A rectangular sheet of perimeter 39 cm and dimensions x cm by y cm is to be rolled into a cylinder as shown in part (a) of the figure. What values of x and y give the largest volume? NOTE: Print the attached word documents for the images (figures referred) of this problem. a) Find the equation of the radius r in terms of pi. b) Find the equation of height y in terms of x. c) Express the equation of the volume in terms of x and y. d) Find the derivative of the Volume that maximize its dimension e) Find the values of x and y that maximize the volume of the cylinder. Hint: Let V' = 0. f) State your conclusion on the meaning of your result from e based on the context of the problem
A rectangular sheet of perimeter 39 cm and dimensions x cm by y cm is to be rolled into a cylinder as shown in part (a) of the figure. What values of x and y give the largest volume? NOTE: Print the attached word documents for the images (figures referred) of this problem. a) Find the equation of the radius r in terms of pi. b) Find the equation of height y in terms of x. c) Express the equation of the volume in terms of x and y. d) Find the derivative of the Volume that maximize its dimension e) Find the values of x and y that maximize the volume of the cylinder. Hint: Let V' = 0. f) State your conclusion on the meaning of your result from e based on the context of the problem
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A rectangular sheet of perimeter 39 cm and dimensions x cm by y cm is to be rolled into a cylinder as shown in part (a) of the figure. What
values of x and y give the largest volume?
NOTE: Print the attached word documents for the images (figures referred) of this problem.
a) Find the equation of the radius r in terms of pi.
b) Find the equation of height y in terms of x.
c) Express the equation of the volume in terms of x and y.
d) Find the derivative of the Volume that maximize its dimension
e) Find the values of x and y that maximize the volume of the cylinder. Hint: Let V' = 0.
f) State your conclusion on the meaning of your result from e based on the context of the problem
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