The area of an annulus refers to the region enclosed by two concentric circles. The calculation logic for the annulus area formula involves decomposing the annulus into two circular components and then computing the difference between their respective areas.
Specifically, the area of the outer circle is first calculated as πR², followed by the area of the inner circle as πr². The area of the annulus is obtained by subtracting these two values, resulting in π(R² − r²).
The formula for the area of an annulus is expressed as: S = π(R² − r²) or S = π(R·R − r·r), where R denotes the radius of the outer circle and r represents the radius of the inner circle.
The derivation of the annulus area formula is achieved through decomposing the annulus into two concentric circles and calculating the difference between their areas. In practical applications, this formula is applicable for computing the area of such objects as tires, pipelines, and annular flower beds.
