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Volume of a paraboloid (Archimedes) The region bounded b

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 82E Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 82E

Volume of a paraboloid (Archimedes) The region bounded by the parabola \(y = ax^2\) and the horizontal line y = h is revolved about the y-axis to generate a solid bounded by a surface called a paraboloid (where a > 0 and h > 0). Show that the volume of the solid is \(\frac{3}{2}\) the volume of the cone with the same base and vertex.

Step-by-Step Solution:

Solution 82E

Step 1  of  2:

In this problem we need to show that the volume of the solid is  the volume of the cone  with same base and vertex.

First we need to find the volume of  the solid that is revolved about the y-axis.

 Given : The  region bounded by the parabola  y = a, and the horizontal line y = h is revolved about the y-axis.

The related graph of The  region bounded by the parabola  y = a, and the horizontal line y = h  is shown below :

Step 2 of 2

Chapter 10.4, Problem 82E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Volume of a paraboloid (Archimedes) The region bounded b