As there are many methods and algorithms to calculate the region's boundary, the volume of the region is based on different shapes or objects. There are mathematical formulas and physics methods that are useful for solving the problems related to cylindrical objects or any other shapes. Among that, one method is known as the shell technique that is useful for the bounded region and spin or extremely thin cylinders about an axis or line.
It is also known as a cylindrical shell method, which is used to find the capacity of a solid of revolution. Rather than, It is used in most special cases when the disk and washer method of calculus is not feasible to solve the problem.
Moreover, you can solve related problems through an online tool to specify the density of solid such as a shell method calculator. So, let's see how to use this shall method and the shell method calculator.
It is a technique to find solids' capacity of revolutions, which considers vertical sides being integrated rather than horizontal ones to simplify some unique problems where the vertical sides are more easily described. Generally, the solid density is the measurement or standard of how much space an object takes up concerning the XYZ axis plane. As unit cubes are used to fill the solid, the volume of solid is measured by the number of cubes.
To solve the problem using the cylindrical method, choose the region or area in the XYZ plane, which is distributed into thin vertical strips. Each vertical strip is revolved around the y-axis, and then the different object of a revolution is obtained which looks like a cylindrical shell. Mostly, It follows the rotation of rectangles about the y-axis.
But, when to use this method? As there is so much confusion in between disk methods and shell methods, when to use which one? Many of us choose the disk formula, as they are not comfortable with the shell formula because they cannot understand what happens in this method, or we can say when to use a cylindrical shell calculator to find out the density. Following are such cases when you can find out volume by shell calculator:
Below given formula is used to find out the volume of region:
V = (R2 -r2)*L*PI
Where,V = volume of solid, R = Outer radius of area, r = Inner radius of region, L = length/height.
Moreover, to find out the surface area, given below formula is used in the shell method calculator:
A = 2*PI*(R+r)*(R-r+L)
Where,A = Surface area, r = Inner radius, R = outer radius, L = height.
Whether you are doing calculations manually or using the shell method calculator, the same formula is used.
Let's see how to use this online calculator to calculate the volume and surface area by following the steps:
Another point to remember that if you are finding the capacity, the length of the area will be considered. If you want to see the surface, then the height of the area will be used. The method is only considered for solids of revolution, which gives the output in the form of volume by shell calculator.
Apart from that, this technique works in a three-dimensional axis to obtain the volume. In this method, if the object rotates a cross-section in the XY-plane around the y-axis, it defines the cylinder shape as it moves in the vertical direction.
Moreover, Suppose the area is cylinder-shaped. In that case, its volume will be the cross-sectional area, multiplying with the height along with the inner radius as well as the outer radius of the cylinder. Typical is calculated by the given formula to determine the size of a solid in this calculator as follows:V = 2π*b∫a*rf(r)dr
Another way to think about the shape with a thin vertical slice is to visualize a vertical cut of a given region and then open it to form a flat plate. After finding the volume of the solid through this calculator, you can depict your problem through the graphical representation. To plot the graph, provide the inner and outer radius and length/height. You will obtain the graphical format of the cylindrical shape when using this calculator.
You have a clear knowledge of how the cylinder formula works for different shapes of solid and how to use this calculator to obtain the volume of the shell from the above explanation.
Shell method is so confusing and hard to remember. Isn't it? We are here with this online tool known as the shell method calculator to make you tension free. Cylindrical Shell