To convert the cylindrical equation $r = 6$ into rectangular coordinates, we use the relationship between cylindrical and rectangular coordinates:

1. In cylindrical coordinates:
   • $r = \sqrt{x^2 + y^2}$

Given that $r = 6$, we substitute this into the rectangular form:

$\sqrt{x^2 + y^2} = 6$

2. Squaring both sides to remove the square root:

$x^2 + y^2 = 36$

Thus, the equation in rectangular coordinates is:

$x^2 + y^2 = 36$

This represents a cylinder with radius 6 centered along the $z$-axis in three-dimensional space.

Would you like further details or have any questions about this conversion?

Here are some related questions that expand on this topic:

1. How do you convert other cylindrical coordinate equations to rectangular form?
2. What is the significance of the $z$-axis in cylindrical coordinates?
3. How would this equation differ if there were a $z$-term in the cylindrical equation?
4. What surfaces do equations of the form $r = k$ (where $k$ is a constant) represent?
5. How would you convert an equation in spherical coordinates to rectangular coordinates?

Tip: Remember that in cylindrical coordinates, $r$ represents the radial distance from the $z$-axis, which is why equations like $r = k$ create cylinders around this axis when converted to rectangular coordinates.