The radius of a circle is 4 feet. what is the area of a sector bounded by a 72° arc?

An angle whose vertex is the centre of a circle and whose sides pass through a pair of points on the circle is called a

central angle. The following symbol, pronounced “theta”, is

used to represent a central angle: .

Each central angle forms an arc length between the points

that it passes through on the circle. The arc length of a circle can be found by first calculating what fraction of the circle is represented by the central angle. Then you find the circumference of the circle. Finally, you find the fraction of that circumference. For example, if a circle has a radius of 10.0 cm and a central angle of 60°, to calculate the arc length for that angle we must first determine what fraction of the circle is represented by the central angle 60°. Since there are 360° in a full circle, we can find the fraction of a circle by simplifying ; The sector represents of the circle. To find the arc length, we now need to find the circumference

of the circle. Circumference of a circle is equal to 2 r.

C 5 2 r

5 2 10.0

62.8 cm The circumference of this circle is about 62.8 cm. To find the arc length, we need to find of 62.8 cm. 62.8 10.5 cm The arc length formed by this central angle is about 10.5 cm.