Explanation Given information: Given, a company packages its powdered diet lemonade mix in containers in the shape of a cylinder. The top and bottom are made of a tin product that costs 5 cents per square inch. The side of the container is made of a cheaper material that costs 1 cent per square inch. The height of any cylinder can be found by dividing its volume by the area of its base. x is the radius of the base (in inches) and the capacity of the container is 120 cubic inches. Calculation: For a cylinder, the top and base are of the shape of a circle. Area of a circle with radius r is given by A = π r 2 Given the height of the cylinder is given by dividing the volume by the area of the base i.e. h = V π r 2 Given radius of the base is x inches i.e. r = x So the area of the base is A = π x 2 The top and base are of same area. Hence the total area of top and base is given by A = 2 π x 2 square inches. Since the top and bottom cost 5 cents per square inch, the cost of top and base together is given by: C 1 = ( 2 π x 2 ) ( 5 ) = 10 π x 2 cents The surface area of the cylinder with base radius r and height h is given by S = 2 π r h< To determine (b) To find the cost of a container whose base is 4 inches in diameter.

2nd Edition

ISBN: 9780321825391

Author: Ratti

Publisher: PEARSON

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Question

Chapter A.3, Problem 71E

To determine

(a)

To write a rational expression in x whose values give the cost of each container, assuming that the capacity of the container is 120 cubic inches.

To determine

(b)

To find the cost of a container whose base is 4 inches in diameter.

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Chapter A.3 Solutions

Precalculus: A Unit Circle Approach

Ch. A.3 - In exercises 10, reduce each rational expression...Ch. A.3 - Prob. 2E Ch. A.3 - Prob. 3E Ch. A.3 - Prob. 4E Ch. A.3 - Prob. 5E Ch. A.3 - Prob. 6E Ch. A.3 - Prob. 7E Ch. A.3 - Prob. 8E Ch. A.3 - In exercises1-10, reduce each rational expression...Ch. A.3 - Prob. 10E

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(a) To write a rational expression in x whose values give the cost of each container, assuming that the capacity of the container is 120 cubic inches.

Solution Summary: The author calculates the cost of a cylinder by dividing its volume by the area of its base.