What Is A Shell Method And How To Use It?

What is a shell method and how to use it?

The shell method is used to find the surface area and volume of solids by the revolution of shells. In the shell method, we integrate along an axis perpendicular to the axis of revolution.

The shell method calculator can solve the shell integration along the axis you want to solve the question. You can get the stepwise volume and surface area of the solid. The shell method is preferred over the washer method, the technique of finding revolution is called the cylindrical shell method.

The shell method is usually preferred when the washer method is hard to apply. The washer method is applied to the donut-shaped cylinder, but the shell method is useful for the vertical cylinder. On the other hand, the disc method is used to find the volume of a vertical cylinder but it is difficult to apply as compared to the shell method. The shell method is going to find the volume parallel to the plan, so you are able to integrate into a three-dimensional plan. That is why the shell method is preferred compared to the washer and disc methods.

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The cylindrical shell method?

The cylindrical shell method is used to find the volume of a solid by its solvation. Consider a two-dimensional area that is bounded by two functions f(x) and g(x). If you are going to rotate the area by the shell method calculus. Then you would be able to draw a three-dimensional shape. This type of shape is called the three-dimensional shape. We call this shape a revolution of the solid and three-dimensional volume. The shell method calculator makes it possible to find the volume of a cylinder in simple steps.

• In the shell method, you break down the solid into infinite shells and align them parallel to the axis of rotation.
• You need to add the volume of all the shells to calculate the volume of the cylinder.
• It is a simple method of finding the volume of a solid as one time you are dealing with a single shell.

Why use the shell method?

You know the surface area of a cylinder is found by multiplying the circumference with the circular base times the height of a cylinder. But by doing this, you are going to ignore the thickness of the cylinder. The well-known formula does not consider the thickness of the cylinder.

The formula for the surface area of a cylinder is:

                                     SA = 2r h

Where, r is the radius and, h is the height of the circular cylinder.

 Now let’s consider the thickness of the cylinder is “w” and the average radius is equal to “p” or the displacement from the axis of rotation. The “h” represents the height of the cylinder. The  shell method calculator makes it possible to find the volume of a cylinder in simple steps

Then we can write the surface area of the cylinder as:

                               SA = 2p h w x

Where:

2p = circumference of cylinder 

h =  height of cylinder 

w = width of cylinder 

x = Change occurring 

Consider, you are revolving around infinite number of cylinders, then the resultant volume of solid is given below:

                    Surface area =    ni=1n2(radius)(height)(thickness)

                  Surface area =    ni=1n2(p)(h)(w) x

By using the formula, ni=1n2(p)(h)(w) x   We are able to measure the volume of the shell for an infinite number of times.  

It is just too easy to find the volume of a cylinder by the shell method calculator. You need to enter the value in the online tool and select the plan of axis. Then enter the lower and upper limit in the calculator, by doing this you can find the volume of the cylinder with the method.                    

Example:

Consider a function f(x)=2x^2+3x^3, the upper and lower limits of the function are “2” and “3” respectively. You are going to integrate the volume with respect to the “x” axis.

 Let the function f(x)=2x^2+3x^3

                                                f(x)=2x^2+3x^3

                                         f(x)   =  232x(3x^3+2x^2)dx

                                            f’(x)   = 2(3x55+x42)+Constant 

The shell method calculator makes it possible to find the volume of the cylinder by entering the function and its axis of plan. You also need to identify the lower and upper limits of the function. 

When to use the shell method?

There are various conditions to use shell method to find the volume of the cylinder:

• You need to use the shell method when the solid is convenient to break down into cylindrical pieces. You need to find the volume of all the cylindrical shapes and then need to add all of them simultaneously.
• Disk method is used when we are able to divide a cylinder into infinitesimally small disks.
• You need to use the washer method when the solid is donut shaped. The height of the donut-shaped cylinder is going to alter gradually.

All three above-mentioned methods are used interchangeably but the shell method is one of the easiest methods to proceed with. You just need to integrate the function corresponding to its upper and lower limit. The disk method is used when we are able to divide a cylinder into a small disk infinitely. You need to use the washer method when dealing with a donut shape.

Conclusion:

The shell method is commonly used to find the volume of a solid around its revolution. You can use the shell method calculator to find the volume of the cylinder. You only have to enter the values of the function and describe its lower and upper limit around the plan of an axis. The method finds the volume perpendicular to the axis of the plan. The method is simpler to apply as compared to the disc and washer methods. It is preferred as you are doing simple integration around a plan of axes.