To find: the rate of change of the volume with respect to radius r at 2 in.
Answer to Problem 30E
The rate of change is
Explanation of Solution
Given information:
Volume of the sphere.
Concept used:
The volume of sphere with radius r is given by:
Instantaneous rate of change of any function f at any point a is given by:
Calculation:
For finding the rate of change of the volume with respect to radius r at 2 in it is enough to find the instantaneous rate of change at
For the function
Hence the instantaneous rate of change is
Chapter 1 Solutions
CALCULUS-W/XL ACCESS
- 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