What is disk washer and shell?

For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.

What is the difference between washer and disk?

A washer is like a disk but with a center hole cut out. The formula for the volume of a washer requires both an inner radius r1 and outer radius r2.

What is difference between Shell and disc?

While the disk method is about stacking disks of varying radii and shape (defined by the revolution of r(x) along the x-axis at each x ), the shell method is about vertically layering rings (defined by 2πx , where x is the radius of the ring) of varying thickness and shape f(x) .

What is Shell formula?

Thus, the volume of the shell is approximated by the volume of the prism, which is L x W x H = (2 π r) x h x dr = 2πrh dr. One cylindrical shell shown in the solid. Finally, the shell method formula is obtained by adding up all of these shell volumes, and allowing dr to get infinitesimally small.

How do you use the washer method?

This application of the method of slicing is called the washer method. The shape of the slice is a circle with a hole in it, so we subtract the area of the inner circle from the area of the outer circle. Example 2) Find the volume of the solid enclosed by the curves y = x and y = x2 when it is rotated about the y-axis.

What is washer method used for?

Use the Washer Method to set up an integral that gives the volume of the solid of revolution when is revolved about the following line . to the axis of rotation. This means that the slices are horizontal and we must integrate with respect to .

How does the washer method work?

The washer method formula

  1. If slices taken perpendicular to the axis of revolution are vertical, then the volume of the solid of revolution is given by.
  2. If slices taken perpendicular to the axis of revolution are horizontal, then the volume of the solid of revolution is given by.