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

To write: The inequalites 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 origin and radius 2.
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casincal
${\mathbb{R}}^{3}$ is the three dimensional coordinate system which contains x, y, and z - coordinates.
The equation $z=8\in {\mathbb{R}}^{3}$ represents the set $\left\{\left(x,y,z\right)|z=8\right\}$, which is the set of all points in ${\mathbb{R}}^{3}$ 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 .
The equation to describe the region of cylinder with center at the origin and radius of 2 units on the xy-plane is ${x}^{2}+{y}^{2}=4$. But, it is required to describe the region in which all points lie on or above the disk in the xy - plane.
The inequality to describe the region of solid cylinder that lies on or above the disk in the xy - plane wiwth center at origin and radius of 2 units ${x}^{2}+{y}^{2}\le 4.$
Thus, the inequality to describe the region of solid cylinder that lies on or below the plane $z=8$ and on or above the disk in the xy - plane with center at the origin and radius