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the length of an arc of a circle is 12cm the corresponding sector is 108cm^2 find the radius of the circle and central angle.

Relevance

Area of the sector = (Area of circle)*[(arc length)/Circumference]

Arc length = A

Area of circle = pi*R^2

Circumference = 2*pi*R

Area of the sector = (pi*R^2)*[A/(2*pi*R)]

Area of the sector = R*A/2

R = 2*(Area of the sector)/A

R = 2*108/12

R = 18 cm

Angle = (Arc length)/R

Angle = 12/18 = 2/3 Radians

Angle = 38.2 degrees

Ceck by calculating the area of the sector from the radius we found above.

area of circle = pi*R^2 = 1017.87602

circumference = 2*pi*R = 113.0973355

(arc length)/circumference = 12/113.0973355 = 0.106103295

(area of circle)*(arc length)/circumference = 108