This is going to seem pretty basic, but I'm trying to figure out if there is a problem in my homework's text or if it's just not clicking for me.
I have to find the volume for the paraboloid $$z = 6 - x^2 - y^2$$
Now the homework problem states: "Before answering the problem, convince yourself that the equation of the paraboloid in cylindrical coordinates is $$z = 6 - r$$
This is where I'm at a loss. I am confident in evaluating the volume integral but I cannot convince myself that z = 6 - r.
Tell me if I'm doing this right or not:
$$ z = 6 - x^2 - y^2 $$ Where: $$ x = r \cos\theta $$ $$y = r \sin\theta$$ Then: $$ z = 6-(r^2(\sin^2\theta + \cos^2\theta)) = 6-r^2 $$ $$ z = 6 - r^2$$
Is that not correct?