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calculate ... go back and calculate
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You have been asked to design a 1-liter cylindrical can made with sheet
aluminum. What dimensions of the can (radius and height) will use the least total
amount of aluminum? State dimensions to the nearest hundredth of a
centimeter.
Hint 1: The aluminum must cover both ends of the can as
well as the circular wall.
Hint 2: 1 liter = 1000 cm^3
I believe my primary equation would be: 2TTr^2 + 2TTrh
I think my secondary equation would be: TTr^2h=1000
Is that right?
I came up with a radius of 12.62 and a height of 2.00
We are supposed to have all of the following...
• Primary equation
• Secondary equation, if applicable
• Statement of domain
• Critical numbers and FDT to establish relative extrema
• Concluding statement(s) to answer the question.
Hello, tradar!
Your answers are correct . . .
You are to design a 1-liter cylindrical can made with sheet aluminum.
What dimensions of the can (radius and height) will use the least total
amount of aluminum?
State dimensions to the nearest hundredth of a centimeter.
Hint 1: The aluminum must cover both ends of the can as well as the wall.
Hint 2: 1 liter = 1000 cm³.
I believe my primary equation would be: .
I think my secondary equation would be: .
Is that right? . . . . Yes!
I came up with a radius of 12.62 and a height of 2.00 . . . . no
We have: . .[1]
Then: .
Differentiate: .
. .
Substitute into [1] and we get: .
Therefore: .