How do you integrate $z^2 = y^2 +x^2$ using cylindrical coordinates?

Question

I'm trying to use: $$\int_{0}^{h} \int_{0}^{2\pi} \int_{0}^{\sqrt{x^2+y^2}}r\:dr\:d\theta\:dz$$ but I'm not totally sure if I should replace the x and y with the $r\:cos(\theta)$ and $r\:sin(\theta)$ respectively that are used for cyllindrical coordinates. It has to be integrated from the $xy$ plane to a height $h$

What should I do?

Answer 1

You can, but be careful with notation. In your integral, $r$ is a variable, but you will integrate from $0$ to $\rho=\sqrt{x^2+y^2}$.