Ring

In geometry, a ring-shaped region is called an annulus. It is formed by taking a larger circle and removing a smaller circle from its center. The two circles have the same center, so they are called concentric circles. The part that remains is the ring: it has a circular hole in the middle and is bounded by two circles.

This shape is different from a disk, which is completely filled inside its outer circle. A ring can be described using two radii: the outer radius, usually written R, and the inner radius, written r. The thickness of the ring is the difference between these two radii, R − r. If the inner radius becomes zero, the hole disappears and the shape becomes a disk.

The area of a ring can be found by subtracting the area of the smaller circle from the area of the larger one. Its formula is A = π(R² − r²), where π is approximately 3.14159. For example, if the outer radius is 5 cm and the inner radius is 3 cm, the area is π(25 − 9) = 16π cm², or about 50.3 cm².

A ring also has two boundary curves: the outer circumference has length 2πR, while the inner circumference has length 2πr. Ring-shaped forms appear in many familiar objects, such as washers, some seals and circular tracks. In mathematics, the annulus is useful for learning how areas can be combined or subtracted and for describing regions between two concentric circles.