Chapter 15, Problem 40RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the given solid.

**40.** Above the paraboloid *z* = *x*^{2} + *y*^{2} and below the half-cone

To determine

**To find:** The volume of the given solid.

Explanation

**Given:**

The region *E* lies above the paraboloid

**Formula used:**

The volume of the given solid is given by,

If
*E* given by

**Calculation:**

Since the equation of the cone is given, use of cylindrical coordinates is a wise choice.

Solve the given equations,

Therefore, *r* varies from 0 to 1,
*z* varies from
*z* varies from
*r.*

Then, by the equation (1), the volume of the given solid is,

Integrate with respect to *z* and apply the limit

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