How do i plot $(r−2)^2 + z^2 \leq 1$?

Question

How can I plot this equation in 3D? Given in cylindrical coordinates. Have tried in wolfram but couldn't work it out..

$$(r−2)^2 + z^2 \leq1$$

Answer 1

You draw a solid disk with radius $1$ at $(x,y,z)=(2,0,0)$ then rotate it a full $2\pi$ radian with respect to $z$ axis.

A solid donut

Answer 2

Parametrize the surface of $$(r−2)^2 + z^2 \leq1$$ as $$r=2\pm \cos(\theta), z=\pm \sin(\theta)$$

for $$0\le \theta \le 2\pi$$

You get a donut shaped solid with the inner radius of one and outer radius of three where $z$ runs from $-1$ to $1$.