Chapter 15.5, Problem 24E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

The figure shows the surface created when the cylinder *y*^{2} + z^{2} = 1 intersects the cylinder *x*^{2} *+ z*^{2}* =* 1. Find the area of this surface.

To determine

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

Explanation

**Formula used:**

The surface area with equation

Here, *D* is the given region.

**Given:**

The surface is the cylinder

**Calculation:**

Solve the given equations,

Since the given surface is the cylinder of radius 1, *x* ranges from 0 to 1 in the first quadrant of the *xy-*plane. So, the total area is 8 times the surface area of the above mentioned region in the first quadrant.

The partial derivatives

Then, by the formula mentioned above, the area of the surface is given by,

Integrate it with respect to *y* and apply the limit

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