# Cylinder sketch in 3-d?

1. Sep 24, 2008

### City88

1. The problem statement, all variables and given/known data

I have to find the volume of the region bounded by a cone and cylinder. (double integral style!)
I usually start off with a sketch, but I can't seem to figure out what this one quadratic surface looks like...

It's a cylinder (in 3-dimensional plane): x2+y2=2ay

3. The attempt at a solution

I know that the equation of a cylinder is just x^2+y^2=a in 3-d. I also know the equations of a hyperbolic, oblique, and parabolic cylinder......but I don't think this is one of those.
Anyone willing to help me out, or at least point me in some sort of direction!
Thanks.

2. Sep 24, 2008

### gabbagabbahey

Try rewriting the equation into standard form:

$$x^2+y^2=2ay$$
$$\Rightarrow x^2+y^2-2ay=0$$
$$\Rightarrow x^2+(y-a)^2-a^2=0$$
$$\Rightarrow x^2+(y-a)^2=a^2$$

Which is the equation of a cylinder of radius a centered at (0,a) running parallel to the z-axis.