For an elliptical cylinder we use the formula for the area of an ellipse instead of a circle before we multiply by the height. The area of an ellipse is (pi)ab where ab replaces r^2 for a circle. The values of a and b are the lengths of the major and minor axes of the ellipse. When a=b we have a circle. So the volume of the cylinder is (pi)abh, where h is the height of the elliptical cylinder. The general rule for finding the volume of an object with a constant cross-section is to multiply the height (length) of the object by the area of its base, which could be circular, triangular, rectangular, square, octagonal, star-shaped, a parallelogram, a mixture, or whatever.