Chapter 14.7, Problem 27E

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11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

Using Cylindrical Coordinates In Exercises 23-28, use cylindrical coordinates to find the indicated characteristic of the cone shown in the figure.

Assume that the cone has uniform density and show that the moment of inertia about the *z*-axis is

To determine

**To prove:** The moment of inertia with respect to the *z*-axis of provided cone is

Explanation

**Given:**

The cylindrical coordinates of the cone indicated by the equation

**Formula Used:**

The moments are found by using the formula:

And the formula of integration:

**Proof:**

The moment of inertia about *z*-axis is represented by

By substituting the values and formula,

It is found that

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