Concept explainers
To Find: The volume of the solid that is obtained by rotating the region that is bounded by the given curves about the specified axis.
Answer to Problem 13RE
The required volume is
Explanation of Solution
Given:
The given expression is
The value of
Calculation:
First find the points of the intersection of the curves
Then
Consider the sketch for the curve is shown in Figure 1
Figure 1
Rotate the shaded region about the y axis as it is rotated in this way a solid is obtained that is cut a slice from the solid horizontal as the washer is obtained.
Consider the outer radius is
The cross sectional area of the washer is,
Consider that,
Then, the volume solid is,
Chapter 6 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