Concept explainers
To express: The volume V of the box as a function of x.
Answer to Problem 59E
The volume of the box as a function of x is
Explanation of Solution
Given:
Dimension of the rectangular piece of cardboard is 12 in. by 20 in.
Side length of the square is x in.
Formula used:
Volume of the rectangle of length l, breadth b and height h is,
Area of the rectangle of length l and breadth b is
Calculation:
Since a square of side length x in. is cut out from each corner, the length and the width of the box are
Hence, the volume of the rectangular box is calculated as follows.
Therefore, the volume of the box as a function of x is
As the dimension of the box cannot take negative values,
Case (i):
Case (ii):
Thus, the domain of the volume function
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