LCKurtz said:This thread is a duplicate of
https://www.physicsforums.com/showthread.php?t=700432
The volume of revolution is the volume of a three-dimensional shape created by rotating a two-dimensional shape around an axis. This is also known as the solid of revolution.
The formula for calculating the volume of revolution depends on the shape being rotated. For example, if a circle with radius r is rotated around the x-axis, the volume can be calculated using the formula V = πr^2h, where h is the height of the shape. Other shapes may require different formulas.
The disc method and shell method are two different approaches to calculating the volume of revolution. The disc method involves slicing the shape into infinitesimally thin discs and adding their volumes, while the shell method involves slicing the shape into infinitesimally thin shells and adding their volumes.
One common mistake is forgetting to convert units. For example, if the radius of a circle is given in inches, but the height is given in feet, the units must be converted before using the volume formula. Another mistake is not considering the limits of integration, which can result in an incorrect volume calculation.
You can check your calculation by using a graphing calculator or a computer program to graph the shape and the volume of revolution. If the calculated volume matches the volume shown on the graph, then the calculation is likely correct. You can also double check your calculation by using a different method, such as the disc method and the shell method, and comparing the results.