You should use the standard formula for volume of a cylinder, except that the height is now the projected height of the axis length onto the perpendicular to the base plane. Thus, if the length of the axis of your cylinder is 10, then the projected height is 10*sin(30deg) = 5 (to see this, consider the projection of the cylinder in the plane: you get a right-angled triangle with hypothenusa 10 and angles 30, 90, 60, in which you need the side opposite to 30deg angle). That should give V = pi*r^2 * 5 = 251.328.
If you find it difficult to understand why it is this way, recall how one can calculate the area of a parallelogram from that of rectangle with equal base length and height: by cutting off one triangle from the rectangle from the left side and pasting it back on the right side, you obtain a parallelogram of equal area. The slanted and straight cylinders are in fact the same: if you project them in the back plane, you see parallelogram and rectangle, respectively. Oop, when writing this I realized I may have made a mistake: it should not have been multiplied by sin(30deg) after all, because of what I just said. The issue is rather how the radius is measured: it is for the cross-section perpendicular to the axis of the cylinder, or is it the radius of the base, which is at an angle to this axis? In the former case, you will need to find the projected radius first.