Chapter 5.2, Problem 62E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

The base of *S* is a circular disk with radius *r*. Parallel cross-sections perpendicular to the base are isosceles triangles with height *h* and unequal side in the base.

(a) Set up an integral for the volume of *S*.

(b) By interpreting the integral as an area, find the volume of *S*.

To determine

**(a)**

**To find:**

An integral for the volume of S

Explanation

**1) Concept:**

Let

**2) Calculation:**

Area of triangle of height h is

where,

Equation of circular disk, centered at origin of radius

Now given that the triangle is perpendicular to the base of a circular disk, so the base of the triangle is at

But,

To determine

**(b)**

**To find:**

The volume of S

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