Chapter 15.5, Problem 11E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the area of the surface.

**11**. The part of the sphere *x*^{2} + *y*^{2}**-** *z*^{2}* = a*^{2} that lies within the cylinder *x*^{2} + *y*^{2} = *ax* and above the *xy*-plane

To determine

**To find:** The area of given surface.

Explanation

**Given:**

The function is the part of the sphere,

The region *D* lies within the cylinder
*xy* plane.

**Formula used:**

The surface area with equation

Here, *D* is the given region.

If
*R* given by

**Calculation:**

Solve the given equation of the function.

Convert the given problems into the polar coordinates to make the problem easier. To obtain the limits, solve the given equations as shown below.

By given the conditions, it is observed that, *r* varies from 0 to

Obtain the partial derivatives of *f* with respect to *x* and *y*.

Then, by the equation (1), the area of surface is given by,

Substitute
*r*

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