6.2 Determining Volumes by Slicing

Learning Objectives • Determine the volume of a solid by integrating a cross-section (the slicing method). • Find the volume of a solid of revolution using the disk method. • Find the volume of a solid of revolution with a cavity using the washer method. In the preceding section, we used definite integrals to find the area between two curves. In this section, we use definite integrals to find volumes of three-dimensional solids. We consider three approaches—slicing, disks, and washers—for finding these volumes, depending on the characteristics of the solid.