To find: The dimensions of the lightest open-top right circular cylindrical can. Also, compare the result with the result obtained in Example 4.
Answer to Problem 16E
Dimensions is
Explanation of Solution
Given information: The volume of open circular cylindrical can is
Concept used: The maximum or minimum value of the function
Calculation:
Consider that the radius of the base of the tank is
The volume of the open tank (V) is written as shown below.
Substitute
Now, write the total surface Area (S) for the given statement.
Differentiate the obtained equation with respect to
Equate the obtained derivative to 0 and solve for
Now, differentiate the equation,
Since at
Substitute
So, the required dimensions is
It is evident from the given example that for the closed can, the dimensions are more.
So, it can be said that the best result is obtained for a shorter can.
Chapter 4 Solutions
AP CALCULUS TEST PREP-WORKBOOK
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning