Explanation Given: A cylinder fuel tank of length L lying on its side, where the ends are circular with radius b . Calculation: Consider acylinder fuel tank of length L lying on its side, where the ends are circular with radius b . Consider the cross-section area of right circularcylinder is A, therefore, the volume of the cylinder is V = A L Using the symmetry the area of cross-section is A = 2 × Area of region A B C Consider the region ABC which is bounded by the curve x = b 2 − y 2

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ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.1, Problem 57PS

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To explain:why the volume of the tank is modeled by V=2L∫−bbb2−y2 .

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Chapter 6.1, Problem 56PS

Chapter 6.1, Problem 58PS

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A manufacturer needs to make a cylindrical can that will hold 1500 cubic centimeters of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction. Hint: Surface area of a cylinder =2πh +2πr^2 Volume of a cylinder =πr^2h

Assignment 10: Problem 8 You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume u=6859. Find the dimensions which minimize the surface area of this box correctly. x=_________ y=_________ z=_________

Answer B b. how do the dimensions of the least expensive can change if the bottom material cost more tha 5 cent per square inch? 7. (a) Determine the dimensions of the least expesive cylindrical can the will hold 100 cubic inches if the materials cost 2 cent , 5 cent and 3 cent, respectively, for the top, bottom ad sides. b. how do the dimensions of the least expensive can change if the bottom material cost more tha 5 cent per square inch?

Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

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why the volume of the tank is modeled by V = 2 L ∫ − b b b 2 − y 2 .

Solution Summary: The author explains that the volume of the cylindrical tank is modeled by V=2Ldisplaystyle underset-boverset

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Chapter 6 Solutions