# Find the volume between a hyperboloid and a cylinder

I'm trying to find the volume bounded by the graphs of $z = 0$ and $z = h$, outside of the cylinder $x^2 + y^2 = 1$, and inside the hyperboloid $x^2+y^2-z^2 = 1.$ I have tried to use cylindrical coordinates, and I got the integral $$\int_0^{2\pi}\int_1^{\sqrt{1+h^2}}\int_0^hr dz dr d\theta$$ However the answer is $h^3\pi/3$, and the integral above computes to $h^3\pi$. I have graphed the region several times and I don't know what I'm doing wrong. Any help will be greatly appreciated.