Question

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

Answer 1

x^2 + y^2 <= 4, 0 <= z <= 8

Explanation:

1. Region that lies on/below the plane means Z<=8
2. Region that lies on/above the xy plane means Z>=0.

Combining 1 and 2, we get

0<=Z<=8

If we want disk of radius 2 in x-y plane to be centered at origin the inequality becomes:

x^2 + y^2 <= 4