Understanding Washers in Mathematics | Definition, Calculation, and Applications

washer

In mathematics, a washer refers to a three-dimensional geometric shape that resembles a cylindrical or circular disc with a hole in the center

In mathematics, a washer refers to a three-dimensional geometric shape that resembles a cylindrical or circular disc with a hole in the center. It is also known as a washer or a cylindrical shell.

To visualize a washer, imagine taking a solid cylinder and hollowing out a smaller cylinder from the center, leaving a hollow ring-shaped object. The outer and inner boundaries of the ring make up the lateral surface of the washer, while the top and bottom faces are circular.

The volume of a washer can be calculated using the formula:

V = π(R^2 – r^2)h

Where:
– V represents the volume of the washer,
– π is a mathematical constant approximately equal to 3.14159,
– R is the radius of the outer circular boundary of the washer,
– r is the radius of the inner circular boundary of the washer, and
– h denotes the height or thickness of the washer.

To find the volume, you subtract the area of the smaller circle (πr^2) from the area of the larger circle (πR^2), and then multiply the difference by the height or thickness of the washer.

The concept of a washer is often used in integral calculus, particularly when integrating to find the volume of a solid with cylindrical or circular cross-sections by using the disk or washer method. It allows mathematicians to approximate the volume by summing up a series of thin slices, where each slice resembles a washer.

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