Calculate the length of an arc of a circle with a radius of 4 cm if its degree measure is 120 °.

| September 3, 2021 | education

Calculate the length of an arc of a circle with a radius of 4 cm if its degree measure is 120 °. What is the area of the corresponding circular sector for a given arc?

Let a circle with a radius R = 4 cm be given, the sector is bounded by an angle of 120 °, we find its arc length and area.
The length of a circular arc is determined by the formula:
l = 2 * π * R, where 2 * π is the angle of the entire circle, 360 °, we have an angle of 120 ° degrees, in radians it is 2π / 3, we substitute in the circumference:
l = 2 * π * R / 3 = 2 * 3.14 * 4/3 = 8.37 cm.
The formula for determining the area of a circle is:
S = π * R², depending on the circumference:
S = (1/2) * (l * R) = (1/2) * (8.37 * 4) = 16.75 cm².
Answer: the area of the sector is 16.75 cm².



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