Question

explore the area of sectors of circles by following these steps.

1. what is the area of circle c? 9π
2. move point a to create a central angle of 180°.

the ratio of the central angle measure to the measure of the entire circle is now 1/2.
the area of the sector created by central angle acb is dropdown the area of the entire circle because the central angle is 1/2 the measure of the entire circle.
dropdown options: 1/4, 1/3, 1/2
m∠acb = 180°
circle diagram with center c, radius 3, points a and b on the circle, angle acb is 180°

Explanation:

The ratio of the central angle to the full - circle angle (360°) determines the ratio of the sector area to the circle area. Here, the central angle \(m\angle ACB = 180^{\circ}\), and the full - circle angle is \(360^{\circ}\). The ratio \(\frac{180^{\circ}}{360^{\circ}}=\frac{1}{2}\). So the area of the sector created by central angle \(ACB\) is \(\frac{1}{2}\) of the area of the entire circle.

Answer:

\(\frac{1}{2}\)