Chapter 15.3, Problem 24E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

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

**24.** Bounded by the paraboloid *z* = 1 + 2*x*^{2} + 2*y*^{2} and the plane *z* = 7 in the first octant

To determine

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

Explanation

**Given:**

The region *D* is bounded by the paraboloid

**Formula used:**

If
*R* given by

If

**Calculation:**

Substitute

So, the value of *r* varies from 0 to

Substitute

Integrate the function with respect to *r* and

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