Given the hyperboloids
$$H_1 := \left\{ (x,y,z) : \frac{x^2}{500} + \frac{y^2}{500} - \frac{z^2}{2000} = 1 \right\}$$
and
$$H_2 := \left\{ (x,y,z) : \frac{x^2}{415} + \frac{y^2}{415}- \frac{z^2}{2000} = 1 \right\}$$
I want to find the volume of a "tower" between the two hyperboloids, i.e., inside $H_1$ and outside $H_2$. The given bounds for both equations is: $-65 \le z \le 15.$
Should I turn the equation into cylindrical coordinates? If so, how? and which equation can I integrate?