Question

The measure of central angle ycz is 80 degrees. circle c is shown. line segments x c, w c, y c, and z c are radii. the length of x c is 9. angle y c z is 80 degrees. sectors x c w and y c z are shaded. what is the sum of the areas of the two shaded sectors? 18 units2 36 units2 45 units2 81 units2f the radius, r? use 3.14 for . round to the nearest inch.

O 12 inches
O 24 inches
O 38 inches
O 46 inches

Answer 1

The sum of the areas of the two shaded sectors is approximately 113 square units.

Step-by-step explanation:

To find the sum of the areas of the two shaded sectors, we need to first calculate the area of each sector. The area of a sector can be found using the formula A = (θ / 360) * π * r^2, where θ is the central angle and r is the radius. Given that the central angle ycz is 80 degrees and the radius xc is 9 units, the area of sector XCW is (80 / 360) * 3.14 * 9^2 = 18π square units. Similarly, the area of sector YCZ is also 18π square units.

Therefore, the sum of the areas of the two shaded sectors is 18π + 18π = 36π square units. Since the question asks for the answer rounded to the nearest unit, the sum of the areas of the two shaded sectors is approximately 113 square units.