   Chapter 12.1, Problem 40E

Chapter
Section
Textbook Problem

# Write inequalities to describe the region.40. The solid cylinder that lies on or below the plane z = 8 and on or above the disk in the xy-plane with center the origin and radius 2

To determine

To write: The inequalities to describe the region of a solid cylinder that lies on or below the plane z=8 and on or above the disk in the xy-plane with the center at the origin and radius 2.

Explanation

3 is the three dimensional coordinate system which contains x, y, and z-coordinates.

The equation z=8 in 3 represents the set {(x,y,z)|z=8} , which is the set of all points in 3 whose z-coordinate is 8 and x, y-coordinates are any values.

The inequality to describe the region in which all points lie on or below the plane z=8 is 0z8 .

The equation to describe the region of cylinder with center at the origin and radius of 2 units on the xy-plane is x2+y2=4

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