Concept explainers
Find the volume of the described solid S.
Answer to Problem 39E
The volume of the described solid S is
Explanation of Solution
Given information: Given curves
Calculation:
Given curves
One cross section (red line segment) is the hypotenuse
Right triangle. The side length
The area of the isosceles right triangle would then be
Solved for
We can use symmetry and double the integral from
The top half of the ellipse only gives us half of
The volume of the solid formed in the integral is of the sum of the area of each triangle .
Thus, the volume of the described solid S 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