Chapter 5.3, Problem 47E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Use cylindrical shells to find the volume of the solid.

A right circular cone with height *h* and base radius *r*

To determine

**To find:**

The volume of the circular cone with the height h and the base radius r.

Explanation

**1) Concept:**

i. If

ii. By the shell method, the volume of the solid by rotating the region under the curve

where,Â

**2) Given:**

The right circular cone with the height h and the base radius r

**3) Calculation:**

The right circular cone with the height h and the base radius r is as shown in the figure. It is obtained by rotating a triangle joining (0,0), (0, h) and (r,0) about y-axis

From the figure, write the equation of line passing through the two points

The slope of the line is

Therefore, the equation of the line is

Using the shell method, find the typical approximating shell with the radius

Therefore, the circumference is

So, the total volume is

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