Chapter 15.6, Problem 45E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Assume that the solid has constant density *k.*

**45**. Find the moment of inertia about the z-axis of the solid cylinder *x*^{2} + *y*^{2} ≤ *a*^{2}, 0 ≤ *z* ≤ *h.*

To determine

**To find:** The momentum of inertia of the solid about the *z*-axis if the solid has constant density *k*.

Explanation

**Given:**

The cylinder is

**Calculation:**

Initially, calculate the moment of inertia over the *z*-axis. Therefore, the integration will be over

The moment of inertia over the *z*-axis is,

Integrate the above integral with respect to *r* and apply the limit of it.

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