Answer
$x^2+y^2\leq4$ and $0\leq z \leq 8$
Work Step by Step
The cylinder extending in the $z$ direction is defined as:
$(x-h)^2+(y-k)^2=r^2$ where $(h,k)$ is the center and $r$ is the radius.
given that the center is the origin $(0,0)$ and the radius, $r=2$,
the cylinder is defined as $x^2+y^2=4$
This $\bf circle$ is the projection of the cylinder onto the $xy$ plane.
But we are told that this is a $\bf solid$ cylinder, so it would include all points inside this circle, defined as $x^2+y^2\leq4$
We are also told that the solid cylinder is bounded by $z=8$ and the $xy$-plane where $z=0$.
So our final answer is:
$$x^2+y^2\leq4$$ $$\bf and$$ $$0\leq z \leq 8$$
