Answer:
38.25 cm²
Step-by-step explanation:
We use the formula for the length of an arc to find the central angle of the sector of the circle.
Then we use the formula for the area of a sector of a circle to find the area.
Length of arc of circle of radius r:
[tex] s = \dfrac{n}{360^\circ}2 \pi r[/tex]
s = arc length
n = measure of the central angle of the sector
[tex] s = \dfrac{n}{360^\circ}2 \pi r[/tex]
[tex] 8.5~cm = \dfrac{n}{360^\circ}2 \pi \times 9.0~cm[/tex]
[tex] n = 54.1^\circ [/tex]
Area of sector of circle of radius r:
[tex] A = \dfrac{n}{360^\circ} \pi r^2[/tex]
A = area of sector of circle
n = measure of the central angle of the sector
[tex] A = \dfrac{54.1^\circ}{360^\circ} \pi (9.0~cm)^2[/tex]
[tex] A= 38.25~cm^2 [/tex]
