Calculate the length of an arc of a circle with a radius of 4cm, if its degree measure is 120 °.
| February 3, 2021 | education
Calculate the length of an arc of a circle with a radius of 4cm, if its degree measure is 120 °. What is the area of the corresponding sector.
A circular arc is the portion of a circle that is enclosed between two radii. To calculate the length of the arc, it is customary to use the formula:
L = πrα / 180 °.
L = 3.14 4 120 ° / 180 ° = 1507.2 ° / 180 ° = 8.37 cm.
A circular sector is a portion of a circle that is placed within two radii and an arc. Its area can be calculated by dividing by two the product of the radius of the circle by the length of its arc:
S = 1 / 2Lr;
S = ½ · 8.37 · 4 = 33.48 / 2 = 16.74 cm2.
Answer: the length of the arc of a given circle is 8.37 cm, and the area of the circular sector is 16.74 cm2.
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