# Calc 2 using washer meathod v.s cylindrical shells

• carlosgrahm
In summary, the washer method and cylindrical shells method are two different approaches used in Calculus 2 to find the volume of solids of revolution. The main difference between them is the shape of the cross-sections used to create the solid. The washer method uses circular cross-sections, while the cylindrical shells method uses rectangular cross-sections. The choice between the two methods depends on the shape of the solid and the ease of setting up the integral. Both methods are equally accurate in finding the volume of solids of revolution. Other methods, such as the disk method and the method of cross-sections, may also be used for finding the volume of solids of revolution, depending on the specific characteristics of the solid.
carlosgrahm
What are the reasons for using washer meathod v.s cylindrical shells?

Cylindrical shells are much easier but there has to be some reason we can always use them

Thanx

carlosgrahm said:
What are the reasons for using washer meathod v.s cylindrical shells?

Cylindrical shells are much easier but there has to be some reason we can always use them

Thanx

Hi carlosgrahm!

(i assume you're talking about finding a volume by integrating)

Sometimes one is easier, sometimes the other.

Do you have a specific problem in mind?

## 1. What is the difference between the washer method and cylindrical shells method in Calculus 2?

The washer method and cylindrical shells method are two different approaches used in Calculus 2 to find the volume of solids of revolution. The main difference between them is the shape of the cross-sections used to create the solid. The washer method uses circular cross-sections, while the cylindrical shells method uses rectangular cross-sections.

## 2. When should I use the washer method versus the cylindrical shells method?

The choice between the washer method and cylindrical shells method depends on the shape of the solid of revolution. If the solid has a hole or empty space in the middle, the washer method should be used. If the solid does not have a hole, the cylindrical shells method should be used.

## 3. How do I set up the integrals for the washer method and cylindrical shells method?

For the washer method, the integral is set up as follows: ∫a^b π(R^2 - r^2)dx, where R is the outer radius, r is the inner radius, and dx represents the width of the solid. For the cylindrical shells method, the integral is set up as follows: ∫a^b 2πrhdx, where r is the distance from the axis of rotation to the edge of the solid, h is the height of the shell, and dx represents the width of the solid.

## 4. Which method is more accurate: washer method or cylindrical shells method?

Both the washer method and cylindrical shells method are equally accurate in finding the volume of solids of revolution. The choice between the two methods depends on the shape of the solid and the ease of setting up the integral.

## 5. Are there any other methods for finding the volume of solids of revolution?

Yes, there are other methods such as the disk method and the method of cross-sections. These methods involve using different shapes for the cross-sections and may be more suitable for certain types of solids. It is important to understand the different methods and choose the most appropriate one for each specific problem.

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