Question

6. A sector of a circle is a region bound by an arc and the two radii that share the arc's endpoints. Suppose you have a dartboard that has a diameter of 20 in and it is divided into 20 congruent sectors. Find the area of one sector.

Part I: Find the central angle. (Hint: A circle has 360 degrees.) (1 point)


Part II: Use your answer from Part I to find the fraction of the circle that one sector will take up. (1 point)


Part III: Use the fractional part from Part II with the area formula to find the area of one sector of the circle to the nearest tenth. (2 points)

Answer 1

A sector of a circle is simply a part of a circle that is enclosed by two radii and a part of the circle's circumference (arc). If the arc makes an angle θ at the center of the circle, then the area of the sector is equal to A=θ360πr2 A = θ 360 π r 2 .

Explanation: