Arcs and Sectors

An arc is a part of the circumference of a circle.
The length of an arc is found by calculating a proportion of the circle’s circumference. If we know the central angle of the arc (in degrees), the formula for arc length is (degree measure of the arc/360) x circumference of the circle.
The sector of a circle is the region enclosed between two radii and the arc joining them. It resembles a piece of pie cut from the circle.
The area of a sector is found by calculating a proportion of the circle’s total area. If we know the angle at the centre of the sector (in degrees), the formula for sector area is (degree measure of the arc/360) x area of the circle.

Calculations Involving Arcs and Sectors

The circumference of a circle is given by the formula 2πr where r represents the radius of the circle.
The area of a circle is calculated using πr² where r is the circle’s radius.
To find the length of an arc, you multiply the central angle by the radius and then multiply that by π/180.
To calculate the area of a sector, multiply the square of the radius by the central angle and then multiply that by π/360.

Arcs and sectors of a circle are measured in relation to the whole circle. A complete circle has 360 degrees.
Arc length and sector area are fractional parts of the circumference and the total area respectively, based on the size of the central angle.
Understanding arcs and sectors forms basis for advanced topics in mathematics like radians and trigonometry.

In real life, arcs and sectors are applied in various ways such as designing arcs and sectors in architectures, in calculating distances in circular race-tracks, etc.
Knowledge of how to calculate arc length and sector area also proves useful in a variety of fields like physics, engineering and computer programming.