To Find: The expression of the volume of a cylindrical shell.
The expression of the volume of the cylindrical shell is
The volume of the cylindrical shell is the product of the circumference area, height, and thickness of the cylindrical shell.
Here, is circumference area, h is the height, and is thickness.
Therefore, the expression of the volume of a cylindrical shell is .
To define: how to find the volume of a solid of revolution using of cylindrical shells.
The region revolved by the rectangles is forms cylindrical shells rather than disks or washers.
After the revolution find the circumference and height of the solid revolution in terms of x and y for a typical shell.
Consider the shell revolved within the limit a and b.
If the rectangle revolved about x-axis then the radius is dy.
If the rectangle revolved about y-axis then the radius is dx.
Therefore, the expression of the volume of a solid of revolution using of cylindrical shells is explained.
To define: shell method is usable method instead of slicing.
The slicing method to find the solid of revolution produces disks and washers sometimes whose radii or difficult to find explicitly. But in the cylindrical shell method forms an easier integral method to find the volume.
Therefore, the shell method is usable method instead of slicing.
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