Question

explore the area of sectors of circles by following these steps. the area of the sector created by central angle acb is 1/2 the area of the entire circle because the central angle is 1/2 the measure of the entire circle. 3. move point a to create a central angle of 90°. the ratio of the central angle measure to the measure of the entire circle is 1/4. the area of the sector created by central angle acb is dropdown the area of the entire circle. options: 1/12, 1/4, 1/2. check. (image: circle with center c, radius cb=3, central angle ∠acb=90°, sector acb shaded.)

Explanation:

Step1: Recall the total angle of a circle

A full circle has a central angle of \( 360^\circ \).

Step2: Calculate the ratio of the central angle to the full circle

The central angle \( \angle ACB \) is \( 90^\circ \). The ratio of the central angle to the full circle is \( \frac{90^\circ}{360^\circ} \).
Simplify the fraction: \( \frac{90}{360}=\frac{1}{4} \).
The area of a sector is proportional to the ratio of its central angle to the central angle of the full circle. So the area of the sector is \( \frac{1}{4} \) of the area of the entire circle.

Answer:

\( \frac{1}{4} \) (corresponding to the option "1/4")