Concept explainers
To find: The function of the surface area of the open rectangular box with a square base in terms of the length of a side of the base and the domain of the function.
Answer to Problem 57E
The formula for the surface area of the open rectangular box as a function of the length of a side of the base is
The domain of the surface area of the open rectangular box as a function of the length of a side of the base is
Explanation of Solution
Given:
The volume of the open rectangular box with a square base is 2 m3.
Formula used:
Volume of the rectangular box of length l, width b, height h is,
Surface area of the open rectangular box of length l, width b, height h is,
Calculation:
Let the length of the open rectangular box be a and the height of the open rectangular box is h.
Since the base of the open rectangular box is a square, the width of the box is same as the length. Therefore, the width of the open rectangular box is a.
Volume of the open rectangular box is,
That is,
Since the volume of the open rectangular box with a square base is 2 m3, the height of the box is computed as follows:
Thus, the surface area of the open rectangular box is
That is,
Substitute the value of h in
Therefore, the formula for the surface area (S) of the open rectangular box as a function of the length of a side of the base (a) is
The domain of the surface area of the open rectangular box as a function of the length of a side of the base is
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- 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