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If we do that and take slices perpendicular to the axis, we will produce a series of discs (like my watermelon example on this page:) **If we rotate an area between 2 curves, and then take slices, we won’t have a discs, instead we’ll have washers** (like the ones given in the pictures at the top of the page above).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) .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 .

Table of Contents

## What the difference between the shell method and disk 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) .

## 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 .

### Disk Washer Method – Calculus

### Images related to the topicDisk Washer Method – Calculus

## How do you know when to use the washer or shell method?

If you want to find the volume of the shape obtained when rotating the region bound by f(x), y=1, and x=2 about the y-axis, then you would use the washer method since the shape you get after rotating has a “hole” in it.

## What is the washer method in calculus?

Washer method: **a method for finding the volume between two functions that are rotated around the x-axis**. **Area of a circle**: pi*r^2. Area of a washer: pi*R^2 – pi*r^2 where R = outer radius and r = inner radius.

## What is shell method used for?

The shell method is a technique for **finding the volumes of solids of revolutions**. It considers vertical slices of the region being integrated rather than horizontal ones, so it can greatly simplify certain problems where the vertical slices are more easily described.

## How does disk method work?

Disk Method

The simplest case is **when R is the area under a curve y = f(x) between x = a and x = b, revolved around the x-axis**. Now imagine cutting the solid into thin slices perpendicular to the x-axis. Each slice looks like a disk or cylinder, except that the outer surface of the disk may have a curve or slant.

## Is washer method parallel or perpendicular?

**two different techniques that can be used to find the volume of a solid of revolution**.

…

Bringing it all together.

Washer Method | Shell Method | |
---|---|---|

Orientation of slices: | perpendicular to the axis |
parallel to the axis |

For vertical slices: | ||

For horizontal slices: | ||

Geometric quantities: | – outer radius | – shell radius |

## See some more details on the topic what is the difference between disk and washer method here:

### AP Calculus Review: Disk and Washer Methods – Magoosh Blog

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 …

### Difference Between Disk And Washer Method? – Ask-rk

The disk method uses an infinitesimally thick slice of the area beneath a curve and rotates it around an axis to create a circle. That’s why you’ll see in …

### Solids of Revolution by Disks and Washers – Math is Fun

In effect this is the same as the disk method, except we subtract one disk from another. … So the Washer method is like the Disk method, but with the inner disk …

### How To Use The Shell Method? (w/ 3 Powerful Examples!)

As the graphic below nicely illustrates, there is a considerable distinction between the disk method and the shell method. … For the disk/washer …

## What is the volume of disc?

The volume of each disk is **πr ^{2}Δx**, where r is the radius of the specific disk and Δx is its height. There are two crucial steps to the problem.

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

**Volume of solids of revolution can be found using following three ways:**

- Disk method.
- Washer method(method of rings)
- Shell method.

## What is the shell method in calculus?

Shell integration (the shell method in integral calculus) is **a method for calculating the volume of a solid of revolution, when integrating along an axis perpendicular to the axis of revolution**. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.

### The difference between disk, washer, and shell method

### Images related to the topicThe difference between disk, washer, and shell method

## How do you do the solid revolution?

To get a solid of revolution we start out with a function, y=f(x) y = f ( x ) , on an interval [a,b] . We then rotate this curve about a given axis to get the surface of the solid of revolution.

## What are the washers?

washer, machine component that is used in conjunction with a screw fastener such as a bolt and nut and that usually serves either to keep the screw from loosening or to distribute the load from the nut or bolt head over a larger area. For load distribution, thin flat rings of soft steel are usual.

## Why is it difficult to use the washer method?

So therefore the inner and outer radius, the inner and outer radius cannot expressed as a function of right? So it is difficult to find the volume using a washer method because **the radius of this expression is not expressed as a function of right**.

## What shape is a washer?

A washer is a thin plate (**typically disk-shaped, but sometimes square**) with a hole (typically in the middle) that is normally used to distribute the load of a threaded fastener, such as a bolt or nut.

## How many integrals would be required in the disk method?

Note: in order to find this volume using the Disk Method, **two integrals** would be needed to account for the regions above and below y=1/2. With the Shell Method, nothing special needs to be accounted for to compute the volume of a solid that has a hole in the middle, as demonstrated next.

## Can volume negative?

Yes, volumes can be 0, but **volumes can never be negative**. The volume of a square is 0, for instance. You might want to look into measure theory and lebesgue measures.

## What is a disk in math?

In geometry, a disk (also spelled disc) is **the region in a plane bounded by a circle**. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not.

## What is disc area?

The area of a disk enclosed by a circle of radius R is **Pi*R ^{2}**. The formula for the circumference of a circle of radius R is 2*Pi*R.

## What is the shell method in calculus?

Shell integration (the shell method in integral calculus) is **a method for calculating the volume of a solid of revolution, when integrating along an axis perpendicular to the axis of revolution**. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.

### Disc/Washer Method vs. Shell Method (rotated about different lines)

### Images related to the topicDisc/Washer Method vs. Shell Method (rotated about different lines)

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

**Volume of solids of revolution can be found using following three ways:**

- Disk method.
- Washer method(method of rings)
- Shell method.

## How do you find the volume of a cross section of a square?

Find the volume of the shape whose base is bound by the function y=−x2+4 y = − x 2 + 4 and lies in the first quadrant using square cross-sections perpendicular to the y-axis. **V=∫baA(y) dy** V = ∫ a b A ( y ) d y .

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