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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 The objective is to minimize the surface area. For minimizing the surface area first find teh critical point by differentiating A with respect to r and equate to 0 Differentiate the following equation with respect to For minimizing the surface area, equate to zero Put this value of in the following equation to find the value ofh Hence, the radius and height of the cylindrical soda can to minimize the surface area are r = 3.83cm and h = 7.67cm

Step 3 of 3

Chapter 4.4, Problem 39E is Solved
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 325 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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