Answer:
Approximately 3.73 square centimeters
Step by step explanation:
To find the area of a sector, you need to know the radius of the circle and the central angle of the sector. In this case, the radius is given as 9 cm, but we need to determine the central angle.
The formula to find the central angle (θ) of a sector is:
θ = (arc length / circumference) * 360°
Given that the arc length is 6 cm and the radius is 9 cm, we can calculate the circumference of the circle using the formula:
circumference = 2 * π * radius
Plugging in the values:
circumference = 2 * 3.14 * 9 cm ≈ 56.52 cm
Now we can calculate the central angle:
θ = (6 cm / 56.52 cm) * 360° ≈ 38.1°
To find the area of the sector, we use the formula:
area = (θ / 360°) * π * radius^2
Plugging in the values:
area = (38.1° / 360°) * 3.14 * (9 cm)^2
area ≈ 3.73 cm^2
Therefore, the area of the sector is approximately 3.73 square centimeters.