Sector, Segment and Arc Length of a Circle

The length of an arc can be determined by a proportion: the arc's degree measure over 360 equals the arc length (L) over the circumference of the circle (2πr). Given the measure of arc JL as 30 degrees and a radius of 8 centimeters, the arc length is calculated to be approximately 4.19 centimeters.

A sector of a circle is defined as the region bounded by an arc and two radii. To find its area, multiply the ratio of the arc's measure (in degrees) over 360 by the area of the whole circle (πr²). An example is given with a radius of 4 meters and an arc measure of 80 degrees, leading to an area of 32/9π square meters or approximately 11.17 square meters.

A segment of a circle is the region bounded by an arc and a chord connecting its endpoints. To find its area, first calculate the area of the sector that includes the segment, and then subtract the area of the triangle formed by the two radii and the chord. An example uses a radius of 5 meters and an arc of 90 degrees, resulting in an approximate area for the segment of 7.135 square meters.