Question

Let r be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when r is revolved about the y-axis?

Answer 1

The shell method is used to find the volume of a solid generated when a region is revolved around an axis. In this case, we are revolving the region bounded by the given curves around the y-axis. To use the shell method, we consider concentric cylindrical shells with thickness dr. The volume of each shell is given by 2πrh * dr, where r is the radius of the shell and h is the height of the shell. We can use integration to sum up the volumes of all the shells to find the total volume of the solid.

Step-by-step explanation:

The shell method is used to find the volume of a solid generated when a region is revolved around an axis. In this case, we are revolving the region bounded by the given curves around the y-axis.

To use the shell method, we consider concentric cylindrical shells with thickness dr. The volume of each shell is given by 2πrh * dr, where r is the radius of the shell and h is the height of the shell.

We can use integration to sum up the volumes of all the shells to find the total volume of the solid.