Concept explainers
a)
To find: The value of
a)
Answer to Problem 12E
The value of
Explanation of Solution
Calculate the value of
Use the below expression for volume.
Differentiate the volume equation.
Substitute the value
The above value of
Therefore,
b)
To show: The rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of the cube and explain geometrically why this result is true.
b)
Explanation of Solution
Each cube will have 6 sides, and area of one side of the cube is
Therefore, the surface area of the cube is as below.
Refer the equation (1).
Simplify the equation as below.
Substitute
Thus, the rate of change of the volume of the cube is approximately half of its surface area.
Assume the condition in which a cube’s side length is x and the change in length of side is
Express the volume change,
The value of
Rewrite the above equation as below.
Hence, the result is geometrically true.
Therefore, the rate of change of the volume of the cube is approximately half of its surface area and the result is geometrically true.
Chapter 3 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