Chapter 15.7, Problem 23E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical coordinates.

23. Find the volume of the solid that is enclosed by the cone z =
*x ^{2}* +

To determine

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

Explanation

**Formula used:**

If
*E* given by

The cylindrical coordinates

**Given:**

The region *E* is enclosed by the cone

**Calculation:**

From the given equations, the value of *z* is obtained below.

And,

It is observed that *r* varies from 0 to 1, and
*z* varies from *r* to

Use the formula mentioned above to change the given problem into cylindrical coordinates. Then, by the equation (1), the volume of the given solid is computed as follows.

Integrate with respect to *z* and apply the limit of it.

Integrate with respect to

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