Chapter 15.7, Problem 24E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical coordinates.

24. Find the volume of the solid that lies between the paraboloid z = *x*^{2} + *y ^{2}* and the sphere

To determine

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

Explanation

**Given:**

The region *E* lies within both the cylinder

**Formula used:**

If
*E* given by

The cylindrical coordinates

**x**

**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

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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