A solid of revolution is a way to find the volume of three-dimensional figures with the help of two-dimensional figures. A solid of revolution can be thought of as a collection of very thin slices. These discs can be looked at as two-dimensional, and when they’re put together, they make up a three-dimensional body. You can also think of them as thin slices of bread that, when put together, make up a loaf of bread. The volume is defined as
|
where
|
Then, taking the final step, the total volume is given by:
Formula
|
Example 1
Find the volume of the solid of revolution about the
Insert what you know into the formula for the volume and calculate:
The volume of the solid is
Example 2
Find the volume of the solid of revolution about the
*
This gives you the equation below that you have to solve for