Shell Method Calculator






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Introduction to the Shell Method Calculator

Shell calculator is an online tool that is used to evaluate the volume of the solid revolution and utilize to integrate it into an axis that is perpendicular to the axis of revolution. This shell method or volume of solid of revolution calculator integrates and uses the provided function to find out the volume of solids by following the step-by-step instructions.

Besides to this, we also have an amazing tool of washer volume calculator that provide volume of solid of revolution in other ways.

What is a Shell Method Volume Calculator?

The shell method calculator is an integration method to estimate the volume. It is used to find the volume of a solid of revolution. This shell method formula calculator integrates the function which is perpendicular to the axis of resolution. The cylindrical shell calculator evaluates the volume by degrading the solids into cylindrical shells.

shell method calculator

On the other hand, if the integrated function will parallel to the axis of rotation then you may try disc integration calculator for the accurate calculation.

Formula Used by Cylindrical Shells Calculator

The shell volume method calculator uses the shell method to integrate functions. In this tool you have to enter your function with the provided limits, it integrates the function using the shell volume method. The shell method volume calculator uses the formula:

$$ V \;=\; 2π \int_a^b xf(x) dx $$

For Example

$$ V \;=\; 2π \int_a^b xf(x) dx $$ $$ V \;=\; 2π \int_2^6 x(x^2+1) dx $$ $$ V \;=\; 2π \int_2^6 (x^3+x) dx $$ $$ V \;=\; 2π \int_2^6 (x^3+x) dx $$ $$ 2π \Biggr[ \frac{x^4}{4} + \frac{x^2}{2} \Biggr]_2^6 $$ $$ 2π \Biggr[ \left( \frac{6^4}{4} + \frac{6^2}{2} \right) \;-\; \left( \frac{2^4}{4} + \frac{2^2}{2} \right) \Biggr] $$ $$ 672π $$

So these are some steps that are follow up while processing results by our tool.

Related: For the conversion of real variable to complex variable function, laplace calculator with steps is a best opinion for professional & students.

How does Cylindrical Shell Method Calculator Work?

The method of this online shell method volume calculator finds the volume of a cylindrical shell of revolution by following these step-by-step:


Firstly, input a given function in the required fields.

Now, add the upper and lower limit that is provided for integration.

Now click on the calculate button to get the solution.


The volume of shell method calculator displays the integration for finding the volume of solid of revolution with a step-by-step solution.

This cylindrical shell calculator does shell calculations very precisely and accurately with the help of the shell method equation.

Moreover, for decomposing the function in terms of frequency & time, you must try our fourier transformation calculator

Benefits of Shell Method Formula Calculator

Volume by cylindrical shells calculator is an online tool that is mainly used to evaluate the volume of a solid of revolution. The volume of the solid of the revolution calculator uses every portion to find out the volume of the whole solid shape. This cylindrical shell volume calculator calculates the volume of the solids concerning the axis perpendicular to the revolution axis of the solid object.

  • The volume of revolution of any solid shape is best evaluated by using this shell method integration tool.
  • Shell method finds the best volume of the revolution for the shapes having no central gaps.
  • The cylindrical shell method calculator is easy to use and understandable.
  • The shell calculator works online and it is free of cost.
  • It calculates the most accurate and precise results with step-by-step instructions.

For the area of irrregular shape, a function is divided into the small chunks which is known as riemann sum. If you wish to approximate area in terms of finite sum, then use limit of riemann sum calculator is the only solution.

How to Find Shell Volume Calculator?

To find the shell method or volume of the solid revolution calculator you have to

  • Open your browser’s home screen.
  • Enter the calculator keywords i.e. cylindrical shell method calculator in the search bar.
  • And search for the results.
  • Now select the required calculator from the Google suggestions.
  • Then enter the values in the required fields along with the provided limits.

This cylindrical shell volume calculator method is easy to use for students and other people. If we try to solve them manually it takes so much time. But online calculators like integral calculator online make it easier and quicker. It helps users to find out about the volume revolution of solids shapes without any real-time issues.

Frequently Asked Question

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

If y is expressed as a washer, then x(y)d is integrated. If Y is expressed as a shell, and y(x)dx is integrated. It totally depends on the function that is designated to it, that is easier and more precise.

Do shell and disk methods give the same answer?

In most calculus books and on websites, there is little data given to show the cylindrical shell method and disk/washer method. It gives the same value when calculating the volume of a solid of revolution. Because both methods are concerned with finding the volume of a solid revolution.

Indeed, it is not rigid that these two definite methods should give the same results.

How do you calculate volume using the shell method?

To find the volume of any solid object by using the shell method, you should cut the shell and lay it flat forming a rectangular solid with length 2πr, height h, and depth dx.

Thus, the volume is V≈2πrh dx.

The same formula is used by method of cylindrical shells calculator to calculate volume by shell method.

Can the volume by shells method be used to find the volume of a non-circular cross section?

Yes, the volume by shells method can be used to find the volume of a solid with non-circular cross-section. In this case, the cross-sectional shape is used to determine the height and width of each shell, and the formula for the volume of a shell is modified accordingly.

However, it is not common to use a "volume by shells calculator" for solids with non-circular cross-sections, as the calculation of volume is more complicated and may involve numerical methods.

How do you set up an integral to find the volume using the method of cylindrical shells?

To set up an integral to find the volume using the method of cylindrical shells, you need to determine the function that describes the shape of each cylindrical shell, the interval over which the integral is taken, and the bounds of integration. The volume of the solid is then obtained by summing up the volumes of all the shells over the interval.

It is not common to use a "cylindrical shells volume calculator" to set up the integral, as not everyone knows about these type of online tools to do calculations.