The resulting slices can be paired so that the two paired slices make a cylinder with radius equal to that of the generating circle and height equal the length cut in the arc of the circle generated by the center of the generating circle.

The sum of these slices will equal the volume of the torus.

Thus the voume of the torus is equal to the volume of the cylinder with base equal to the generating circle (disc) and height equal to the circumference of the circle generated by the center of the generating circle.

theVolume is (pi)r