What is the Area of a Washer?

The exact area of a washer, also known as an annulus, is found by subtracting the area of the inner circle from the area of the outer circle. Based on the reference provided:

The formula for the area of a circle is π * r². So the area of the washer is π * R² - π * r², where R is the outer radius and r is the inner radius.

Understanding the Washer Area Formula

A washer is essentially a flat ring-shaped object, like a coin with a hole in the middle. To find its area, we consider it as a large circle with a smaller circle removed from its center.

Key Components

Here's a breakdown of the formula components:

• R: The radius of the outer circle (from the center to the outer edge of the washer).
• r: The radius of the inner circle (from the center to the inner edge of the hole).
• π (Pi): A mathematical constant approximately equal to 3.14159.

The formula calculates the area of the larger circle (πR²) and then subtracts the area of the smaller circle (πr²), leaving the area of the ring shape.

How it Works

Think of cutting out a large circle from paper. Its area is πR². Now, cut a smaller circle out of the center of the large circle. The area of the part you removed is πr². The area of the remaining paper (the washer shape) is the original large area minus the removed small area: πR² - πr².

This can also be factored for convenience: π(R² - r²). Both forms of the formula yield the same result.

Example Calculation

Let's find the area of a washer with an outer radius (R) of 5 cm and an inner radius (r) of 2 cm.

• Area of outer circle = π * (5 cm)² = 25π cm²
• Area of inner circle = π * (2 cm)² = 4π cm²
• Area of washer = 25π cm² - 4π cm² = 21π cm²

Using the factored form:

• Area of washer = π * (5² - 2²) cm² = π * (25 - 4) cm² = π * 21 cm² = 21π cm²

The area is approximately 21 * 3.14159 ≈ 65.97 cm².

Summary Table

Calculating the area of a washer is a straightforward application of the basic circle area formula.