Chapter 15.5, Problem 23E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the area of the finite part of the paraboloid *y* = *x*^{2} *+ z*^{2} cut off by the plane *y =* 25. [*Hint:* Project the surface onto the xz-plane.]

To determine

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

Explanation

**Formula used:**

The surface area with equation

Here, *D* is the given region.

If
*R* given by

If

**Given:**

The finite part of the paraboloid,

**Calculation:**

From the hint given in the problem, project the region onto the *xz-*plane that is substitute
*xz-*plane, the region is the circle of radius 5. So, use polar coordinates to evaluate the area of the region.

The partial derivatives

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

Since the equation involves only *x* and *z*, substitute

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