Disk Method Calculator

Want to calculate the volume of a cylindrical shape of a cross sectional area? Use the Disk Method Calculator as it calculate such problems for free.

Upper Function:

Lower Function:

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Introduction to Disk Method Calculator:

Disk method Calculator is an amazing tool that helps you evaluate the volume of a cylindrical shape in a cross-sectional area. It is used to find the volume of a sphere that is rotating along a perpendicular axis.

Disk Method Calculator with Steps

The disc method calculator is the best online source for students, professionals, or teachers because they want a reliable tool that gives them an accurate solution to disk method problems without any man-made mistakes.

What is Disk Method?

Disk method is a process of finding the volume of a sphere that is rotating along a perpendicular axis in a cross-sectional area in three dimensions. It is used to find the rotational mass of a solid at the perpendicular axis of rotation for circular shapes.

The formula of the disk method uses the definite integral that represents the given area as bounded over an interval [a,b] and π is the constant term. The disk washer method calculator uses the following formula to solve the complex problems,

$$ V \;=\; \pi \int_a^b [f(x)]^2 dx $$

How to Find Volume Using the Disk Method?

The disk washer calculator is used to find the volume of rotation of a cross-sectional area with the help of the integration method. If you solve the volume of a rotating sphere without using the disk method it would be difficult for you to get a solution. That means the disk method gives a way to easily solve the volume of a sphere in 3-D space.

Now let us see an example of the volume of a rotating disk with a solution to give you a clear understanding of disk method calculation. The disk method calculator can help you solve the volume of the cylindrical shape in seconds. So an example is given below,

Example: Find the volume of solid formed by revolving the curve y = 1/x from x = 1 to x = 2 around the x-axis.

Solution:

Step 1:

Identify the Function f(x) or g(y)and the Interval[a,b] on which it is being rotated in the given region.

f(x)=1/x and interval a=1 and b=2

Step 2:

The disk method formula is,

$$ V \;=\; \pi \int_a^b [f(x)]^2 dx $$

Step 3:

Put the function and the limit values in the above disk formula such as,

$$ =\; \pi \int_1^2 \biggr(\frac{1}{x} \biggr)^2 dx $$

Step 4:

Simplify the above expression to make the integration process smooth,

$$ =\; \int_1^2 \frac{1}{x^2} dx $$

Step 5:

Integrate the given function with respect to integration variable x.

$$ =\; \pi \left[ -\frac{1}{x} \right] \biggr|_1^2 $$

Step 6:

Apply the upper and lower limits to a solution to your given disk method problem.

$$ =\; \pi \left[ -\frac{1}{2} - (-1) \right] $$

$$ =\; \frac{\pi}{2} units^3 $$

How to Use the Disk Method Calculator?

The disc method calculator has a simple layout that helps you to understand how to use it for evaluating the volume of a rotational sphere of a given region, only by following some simple steps that are:

Enter the function f(x) that you want to evaluate the volume of cross-sectional area in the input field.
Enter the integration variable of a disk method in the input field.
Add the upper and the lower limit of the disk method in the next input box.
Review the given disk method problem before hitting the calculate button to start the evaluation process in the disk washer method calculator.
Click the “Calculate” button to get the result of your given Disk method problem.
If you are trying our volume of a disk calculator for the first time then you can use the load example to learn more about this method.
Click on the “Recalculate” button to get a new page for finding more example solutions to Disk method problems.

Output from Disc Method Calculator:

Disk method Calculator with steps gives you the solution from a given input value in it and it gives you with solutions that have:

Result Option

When you click on the result option the volume of the disk calculator gives you a solution to the given problem.

Possible Steps

When you click on it, this option will provide you with a solution where all the calculations of the Disk method process are mentioned in detail

Useful Features of Disk Washer Method Calculator:

The disk washer calculator gives you useful features that help you to evaluate the volume of rotation of a sphere in cross-section area problems and give you a solution without any trouble. You just need to put the input values and get the solution instantly. These features are:

The disc method calculator is a free-of-cost tool so you can use it for free to find disk method problem solutions without fee.
It is an adaptable tool that can manage various types of volume rotation in a given region to get solutions
Our volume of a disk calculator helps you to get conceptual clarity about the disk method process when you use it to practice multiple examples.
It is a swift tool that gives you solutions to disk method problems even if it is a complex problem in a few seconds.
The volume of disk calculator is a reliable tool that provides you right solutions whenever you use it to calculate the disk method
Disk method Calculator provides the solution without saying for signup option which means you can use it multiple times in a day to get the solution.

Related References

How would you define disk method?
Explain the volume of revolution using disk method:
Give some examples of disk method:
Give an overview of disk method?

Frequently Ask Questions

What is the difference between disk and washer method

The disk and washer methods are techniques used in calculus to find the volume of a solid of revolution. Here are the main differences between the two methods:

The disk method involves slicing the solid perpendicular to the axis of revolution, creating a series of disks (or circles).The washer method is similar to the disk method, but it accounts for solids with a hole in the middle, creating a washer shape (a disk with a hole)
This method is used when the solid has no hole or gap (i.e., it is a solid cylinder or a solid ).This method is used when the solid has a hole or gap (i.e., it is a hollow cylinder or a hollow cone).
It used for solids without a hole; integrates the area of disks but the washer method used for solids with a hole; integrates the area of washers.

Is the shell method the same as the disk method

No, the shell method is different from the disk method. Both methods are used to find the volume of a solid of revolution, but they involve different approaches. Here's a comparison of the shell method and the disk method:

The shell method involves slicing the solid parallel to the axis of revolution, creating cylindrical shells.This method is more convenient when the function is easier to integrate using shells, particularly when the height of the shell is simpler to express as a function of the variable of integration.

The disk method involves slicing the solid perpendicular to the axis of revolution, creating a series of disks (or circles).This method is used when the solid has no hole or gap and is easier to apply when the radius of the disk can be directly expressed as a function of the variable of integration.

When to use disk vs shell method

While Choosing between the disk and shell methods depends on the specifics of the problem for simplifies the integration process. Here are some guidelines to help decide when to use each method:

Disk Method

The solid of revolution is created by rotating a region around an axis that is either a boundary of the region.The region being rotated is simple to describe with respect to the axis of rotation.The axis of rotation is either along the boundary of the region or is the region itself.

Shell Method

The solid of revolution is created by rotating a region around an axis that is not a boundary of the region, or when the function describing the region is more complicated to express perpendicular to the axis of rotation.

When you have problems where the height of the cylindrical shells (difference between the outer and inner functions) can be easily expressed as a function of the variable of integration.

Are disk and washer method the same

The disk and washer methods are closely related, but they are not exactly the same. Both methods are used to find the volume of a solid of revolution, but they apply to slightly different scenarios:

Disk Method

The disk method involves the solid that is perpendicular to the axis of revolution, creating a series of disks (solid circles).This method is used when the solid has no hole or gap (i.e., it is a solid cylinder or a solid cone).

The volume V is found by integrating the area of these disks along the axis of revolution.
For a solid revolved around the x-axis:

$$ V \;=\; \pi \int_a^b [(R(x))]^2 dx $$

Washer Method

The washer method is similar to the disk method, but it used for solids with a hole in the middle, creating a washer shape (a disk with a hole).This method is used when the solid has a hole or gap inside the objective.

The volume V is found by integrating the area of the washers along the axis of revolution.
For a solid revolved around the x-axis:

$$ V \;=\; \pi \int_a^b [(R_{outer} (x)]^2 - [R_{inner} (x)]^2 dx $$

How to know when to use disk or washer method

To determine when to use the disk or washer method to find the volume of a solid of revolution, or the axis of rotation in three dimension space. Here are some reason that tell you about the use the disk and washer method.

Use the disk method when the solid does not have a hole in the middle of a objective. when you are revolving a region around an axis that lies on the boundary of the region

Use the washer method when the solid has a hole in the middle. When you are revolving a region around an axis that does not lie on the boundary of the region or when the region itself has an inner boundary.

Amanda Jepson

Last Updated February 21, 2024