Write an inequality to describe the region. The solid cylinder that lies on or below the plane z = 9 and on or above the disk in the xy-plane with center the origin and radius 3

0 ≤ z ≤ 9, x^2 + y^2 ≤ 9

Step-by-step explanation:

z = 9

radius = 3

The region that lies on or below has a plane z = 9

This means that z ≤ 9

The region that lies on or above the disk in the xy plane is described by z ≥ 0

The combination inequality is 0 ≤ z ≤ 9

To restrict the disk centred at the origin with radius 3 is to restrict the x and y values. We have

x^2 + y^2 ≤ r^2

x^2 + y^2 ≤ 3^2

x^2 + y^2 ≤ 9

The full set of inequalities is

0 ≤ z ≤ 9, x^2 + y^2 ≤ 9