Area and Volumes of Revolution

Definition

The area and volumes of revolution refer to finding the area or volume generated when a region bounded by a curve is rotated around an axis. This concept involves integrating functions with respect to either x or y to calculate these quantities.

Related terms

Disk Method:

The disk method is a technique used to find the volume of revolution by considering the cross-sections of the solid as disks or washers perpendicular to the axis of rotation.

Shell Method: The shell method is an alternative technique for finding volumes of revolution. It involves considering cylindrical shells parallel to the axis of rotation and integrating their volumes.

Washer Method:

The washer method is another approach for finding volumes of revolution. It uses washers (rings) instead of disks or shells, allowing for more complex shapes to be calculated.