The area of a sector of a circle with a radius of 4 centimeters is 2.512 square centimeters.

Question

The measure of the angle defining the sector is what in degrees

Answer 1

Calculate the area of sector of a circle by using formula : A = (θ/360) * πr², where θ = central angle in degrees and r = radius.

To find the measure of the angle, substitute A = 2.512 cm², r = 4 cm and π = 22/7 in the above formula.

2.512 = (θ/360) * (22/7)(4)²

(2.512 * 7 * 360) / (22 * 16) = θ

6478.92 / 352 = θ

17.98 = θ

The angle is 17.98^o.