First you have to know/state what kind of surface of revolution you have to calculate the volume for (hyperboloid of one or of two sheets). The formula you gave assumes revolution around the x-axis. Where are the axis in your drawing? Given the usual arrangements of axis this would mean a hyperboloid of two sheets but then it would be absolutely unclear which volume should be calculated as the drawing is not symmetrical with respect to the horizontal x-axis.
You can't calculate anything as long the goal is not clearly specified and as long as the drawing and its dimensioning does not fit the equation given. Either one of the two is either wrong or approximated in such a manner that it can't be told what dimension we should rely on - diameters (x-values) or heights (y-values).
I guess that you are supposed to calculate the volume of a hyperboloid of one sheet like in the plot below. As of the axis we assume y-axis going up, x-axis to the right and z to the front. You slice your volume in a lot (infinite number) of tiny, cylindrical slices like the red one in the plot below. The radius of the red cylinder is (using the aforementioned convention) x, the height is an infinite small y-difference dy. So the volume of a single red slice is x^2*pi*dy. Now you have to sum up (integrate) all those slices from y=ybottom to y=ytop and we get for the volume V=pi*int(x^2)dy from ybottom to ytop.
To calculate it you mus express x^2 in terms of y, which is pretty easy with the given equation.
To get the limits you will have to dissolve the conflict drawing dimensioning versus equation given.
EDIT: As the insertion of a pic in the text seems not to work again, I make it an attachment
To give you an idea about the difference you get using either the dimensioning or the given equation:
1) If we assume that the values for A,B,C,D and E are correct, we get a slighty different equation (564.06 instead of 560 and 3582.67 instead of 3600) and the volume is 322944,86 m^3
2) If we assume the given equation is correct and also the values for A and E, we would get different values for B,C and D and the volume is 325346.89 m^3.
Thats a difference of approx. 2400 m^3!
A third way to interprete the given sheet would be to assume that the equation, the sum C+D and either A OR E are correct, but I couldn't be bothered to try these variants, too.