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A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters.

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A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 60 per square centimeter, while the sides are made of material that costs 4¢ per square centimeter.

(a) Express the total cost C of the material as a function of the radius r of the cylinder. (Refer to Figure 43.)

Figure 43

Top Area = mr2 Lateral Surface Area = 2mrh Area = r2 Bottom


(b) Graph C = C(r). For what value of r is the cost C a minimum?

Transcribed Image Text:

Top Area = mr2 Lateral Surface Area = 2mrh Area = r2 Bottom

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a b Graphing Using MIN…View the full answer


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Related Book For  answer-question
Precalculus

Precalculus

ISBN: 978-0321716835

9th edition

Authors: Michael Sullivan

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Question Details
Chapter # 4
Section: Section 4.3
Problem: 55
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Question Posted: January 10, 2019 06:25:45
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The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.

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