Can you tell me where did 18 pi come from ?skeeter said:
jaychay said:
The shell method involves using the radius of a cylindrical shell to find the volume of a solid of revolution, while the disk method involves using the radius of a disk to find the volume. The shell method is typically used for solids with a hole in the middle, while the disk method is used for solids without a hole.
As mentioned before, the shell method is best used for solids with a hole in the middle, while the disk method is used for solids without a hole. Additionally, the shape of the solid of revolution can also determine which method is more appropriate to use. It is recommended to visualize the solid and determine which method would be more efficient in finding the volume.
The formula for finding volume using the shell method is V = 2π∫(radius)(height)(thickness)dr, where the radius is the distance from the axis of revolution to the shell, the height is the height of the shell, and the thickness is the difference between the outer and inner radius of the shell.
The formula for finding volume using the disk method is V = π∫(radius)^2dx, where the radius is the distance from the axis of revolution to the disk and dx is the width of the disk. This formula can be used for both solids with a hole and without a hole.
The shell and disk method can be used for any shape that can be formed by rotating a function around an axis. This includes shapes such as circles, parabolas, and hyperbolas. However, the methods may be more complex for certain shapes and may require additional calculations.