Concept explainers
To evaluate: the integral to obtain the expression for the volume of the sphere of radius R .
Answer to Problem 50E
Explanation of Solution
Given:
Thevolume of the sphere of radius Rcan be found by slicing the sphere vertically.
The radius of cross-section in the below figure is
The process in the result of integral is.
Calculation:
As thegiven function is
According to the question
Hence,the derivative of the given functionis
Chapter 15 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus: Early Transcendentals (2nd Edition)
University Calculus: Early Transcendentals (3rd Edition)
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