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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 6, Problem 4RCC

(a)

To determine

**To Find:** The expression of the volume of a cylindrical shell.

Expert Solution

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, *h* is the height, and

Therefore, the expression of the volume of a cylindrical shell is

(b)

To determine

**To define:** how to find the volume of a solid of revolution using of cylindrical shells.

Expert Solution

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.

(c)

To determine

**To define:** shell method is usable method instead of slicing.

Expert Solution

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.