A solid of revolution is a three-dimensional object obtained by rotating a two-dimensional region around an axis. The volume of such solids can be calculated using integration techniques.
5 Must Know Facts For Your Next Test
The Disk Method is used when the solid is formed by rotating a region around the x-axis or y-axis, creating cylindrical disks.
The Washer Method extends the Disk Method to accommodate holes in the middle of the solid, resulting in washers instead of disks.
The Shell Method involves slicing the solid into cylindrical shells and is particularly useful when rotating around an axis parallel to the boundaries of the region.
A common formula for volume using the Disk Method is $V = \pi \int_a^b [R(x)]^2 dx$, where $R(x)$ is the radius of each disk.
The Shell Method formula for volume is $V = 2\pi \int_a^b rh dx$, where $r$ is the radius and $h$ is the height of each shell.