Volume of a Solid, $x^2 - y^2 = a^2$ The question is

Find the volume of a solid rotated around the y axis, bounded by the given curves: $$x^2 - y^2 = a^2$$
$$x = a + h$$

I am lost by the number of variables in this question and the question does not tell me what kind of variables they are, only that they are both greater than 0.

This is known as a hyperboloid of revolution of one sheet. 
Forget the second equation, it only means that to get both x and y real, x should be equal or grater than a by a small amount h. $y > x$ always in the first quadrant for a quarter branch of this (rectangular) hyperbola.The limits of y are $0$ and $y_1$ in:
$$ x^2 = y^2 +1 $$
$$ V = \pi \int x^2 dy = \pi \int_0^{y1} (1+y^2) dy,   $$ where I  have chosen $y $ as the independent variable. And you can take it from there.
