The length of the arc of the circle on which the central angle of 60 degrees rests is 2 cm.

The length of the arc of the circle on which the central angle of 60 degrees rests is 2 cm. Find the radius of the circle to the nearest 0.01 cm and the area of the sector formed by this angle to the nearest 0.1 cm2.

Arc length formula in terms of center angle:

L = п R * a / 180 °, where R is the radius of the circle; a – the value of the central angle in degrees,

a = 60 °; that is, L = п R / 3; from here:

R = 3 L / п; = 3 * 2 / 3.14 ≈ 1.91 (cm);

Area of a sector formed by an angle of 60 °:

S = п R² / 6 = 3.14 * 1.91² / 6 ≈ 1.9 (cm²);

Answer: R ≈ 1.91 cm; S ≈ 1.9 cm².