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Optimal soda can a. Classical problem Find the radius and

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 39E Chapter 4.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 39E

Optimal soda can a. Classical problem Find the radius and height of a cylindrical soda can with a volume of 354 cm3 that minimize the surface area. b. Real problem Compare your answer in part (a) to a real soda can, which has a volume of 354 cm3, a radius of 3.1 cm, and a height of 12.0 cm, to conclude that real soda cans do not seem to have an optimal design. Then use the fact that real soda cans have a double thickness in their top and bottom surfaces to find the radius and height that minimizes the surface area of a real can (the surface areas of the top and bottom are now twice their values in part (a)). Are these dimensions closer to the dimensions of a real soda can?

Step-by-Step Solution:

Solution 39E Step 1: (a) Consider a cylindrical soda can with the volume of cm . Let the radius of the cylinder be and eight be . Consider that the volume of the cylinder with radius and height is given by the following formula V = r h2 …(1) So, in this case volume is, V = r h = 354 h = r2 Now, the total surface area of the cylinder with radiusr and heighth is given by the following formula A = 2r +2rh ….(2)

Step 2 of 3

Chapter 4.4, Problem 39E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Since the solution to 39E from 4.4 chapter was answered, more than 438 students have viewed the full step-by-step answer. This full solution covers the following key subjects: real, soda, radius, height, surface. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Optimal soda can a. Classical problem Find the radius and height of a cylindrical soda can with a volume of 354 cm3 that minimize the surface area. b. Real problem Compare your answer in part (a) to a real soda can, which has a volume of 354 cm3, a radius of 3.1 cm, and a height of 12.0 cm, to conclude that real soda cans do not seem to have an optimal design. Then use the fact that real soda cans have a double thickness in their top and bottom surfaces to find the radius and height that minimizes the surface area of a real can (the surface areas of the top and bottom are now twice their values in part (a)). Are these dimensions closer to the dimensions of a real soda can?” is broken down into a number of easy to follow steps, and 134 words. The full step-by-step solution to problem: 39E from chapter: 4.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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