Chapter 16.6, Problem 25E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find a parametric representation for the surface.

**25.** The part of the cylinder *x*^{2} +* y*^{2} + *z*^{2} = 36 that lies between the planes *z* = 0 and *z* = 3

To determine

**To find:** The parametric representation for the part of the sphere

Explanation

**Given data:**

The equation of part of the sphere is given as follows.

From the equation of the sphere, the radius of the sphere is 6.

The required part of the sphere lies between the planes

**Formula used:**

Write the expression for parametric equations of the sphere with radius

Here, the limits of

**Calculation of parametric equations of the sphere:**

Substitute 6 for

**Calculation of**
** limits:**

As the required part of the sphere lies between the planes
*z*-parameter to the given values and find the lower and upper limits of

**Case-i:** If

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