Question

Write an inequality to describe the region. The solid cylinder that lies on or below the plane z = 4 and on or above the disk in the xy-plane with center the origin and radius 2?

Answer 1

The inequality that describes the region is x^2 + y^2 ≤ 4 and z ≤ 4.

Step-by-step explanation:

We can describe the region using an inequality involving the z-coordinate and the equation of the disk. The equation of the disk in the xy-plane with center at the origin and radius 2 is x2 + y2 ≤ 22 or x2 + y2 ≤ 4. The inequality for the solid cylinder lying on or below the plane z = 4 is z ≤ 4.

Therefore, the inequality that describes the region is x2 + y2 ≤ 4 and z ≤ 4.