Find eqn of cylinder of height

[DryRun]

Homework Statement

How to find the equation of cylinder: $x^2+y^2=4$ from z=0 to z=2?

Homework Equations

$$(x-a)^2+(y-b)^2=r^2$$

The Attempt at a Solution

I can't figure out how to implement the z-coordinate into the general equation of cylinder. In the latter, the height is taken as infinite in both opposite directions (upward and downward).

 

[Mark44]

Homework Statement

How to find the equation of cylinder: $x^2+y^2=4$ from z=0 to z=2?

Homework Equations

$$(x-a)^2+(y-b)^2=r^2$$

The Attempt at a Solution

I can't figure out how to implement the z-coordinate into the general equation of cylinder. In the latter, the height is taken as infinite in both opposite directions (upward and downward).

Doesn't this work?
$x^2+y^2=4; 0 \leq z \leq 2$

 

[DryRun]

Hi Mark44!

Actually, that's how the equations are originally given in the problem but i was wondering if there is a way to combine those 2 into a single equation, since the height of the cylinder is known.

In my mind, maybe something like that: $x^2+y^2 + (z-c)^n=4$ even though it's now become closer to a sphere!

 

[Mark44]

No, there's no way to combine the equation and inequality into one.