Chapter 15.3, Problem 21E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use polar coordinates to find the volume of the given solid.

**21.** Below the plane *2x* + *y* + *z* = 4 and above the disk *x*^{2} + *y*^{2} ≤ 1

To determine

**To find:** The volume of the given solid by using polar coordinates.

Explanation

**Given:**

The region *D* lies below the plane

**Formula used:**

If
*R* given by

**Calculation:**

From the given region *D*, it is observed that the value of *r* varies from 0 to 1 and the value of

Substitute

Integrate the function with respect to *r* and apply the limit.

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