Disc method:

Disk integration is a means of calculating volume of a solid of revolution, while integrating along the axis of revolution. This method models the generated three dimensional shapes as a "stack" of an infinite number of disks of varying radius of infinitesimal thickness.

To find volume of the solid of revolution with the disc method, use one of the following.

Horizontal axis of revolution                            
Vertical Axis of Revolution                         

"Hollow" solid of revolutiona solid of revolution is a solid figure obtained by rotating a plane curve around some straight line that lies on the same plane. The two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration. To apply these methods, it is easiest to draw the graph in question, identify the area that is actually being revolved about the axis of revolution, and then draw a straight line, vertical for functions defined in terms of x and horizontal for functions defined in terms of x, which is referred to as a slice. The disc method is used when the slice that was drawn is perpendicular to the axis of revolution; that is, when integrating along the axis of revolution.

The method is visualized by considering a thin vertical rectangle at x between y = f(x) on top and y = g(x) on the bottom, and revolving it about the x-axis; it forms a ring (or disc in the case that g(x) = 0), with outer radius f(x) and inner radius g(x). Adding up all of the areas along the interval gives the total volume. Alternatively, where each disc has a radius of f(x), the discs approach perfect cylinders as their height dx approaches nearly zero. Assume that we are given an area bounded by certain curves in xy-plane. That particular area can be rotated around an axis to form a solid. Each point of figure can be rotated in a circle. If you slice the solid perpendicular to the axis you will see a "cross section" (the area revealed by the slice) that is either a full disk or a "washer" (the area between 2 circles. It's easy to calculate area of the circle and you can imagine the solid as made of a lot of quite thin circles.