What does the disk method do?

The disk method is a slicing technique that creates cross sections of a solid of revolution by slicing perpendicular on the axis of rotation and calculating the volume of the solid by adding the volumes of the infinitely many thin cross-sections.

Is shell method the same as disc method?

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) .

How do you calculate disk method?

The volume of a disk is typically found using the same formula as a cylinder: V=πr2h V = π r 2 h . The integral in the disk method formula sums the volume of the disks that create the three-dimensional shapes (similar to how the area under a curve can be measured with rectangles).

What are the three methods of finding the volumes of solids of revolution?

Volume with washer method: revolving around x- or y-axis

  • Solid of revolution between two functions (leading up to the washer method) Generalizing the washer method. Practice: Washer method: revolving around x- or y-axis.
  • Volume with washer method: revolving around other axes.

What is r in shell method?

Key Idea 25: Shell Method. Let a solid be formed by revolving a region R, bounded by x=a and x=b, around a vertical axis. Let r(x) represent the distance from the axis of rotation to x (i.e., the radius of a sample shell) and let h(x) represent the height of the solid at x (i.e., the height of the shell).

How do you do 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.

How do you find volume using the disk method?

The disk method is used when the axis of revolution is the boundary of the plane region and the cross-sectional area is perpendicular to the axis of revolution. This method is used to find the volume by revolving the curve y=f(x) y = f ( x ) about x -axis and y -axis.