Respuesta :
Answer:
Arc length of circle with circumference 18 and an arc with a 120° central angle is:
6
Step-by-step explanation:
The arc length of a cicle is given by:
[tex]2\pi r\times \dfrac{\theta}{360\°}[/tex]
Here, circumference=18
i.e. 2πr=18
and [tex]\theta=120\°[/tex]
Arc length=
[tex]18\times \dfrac{120\°}{360\°}\\ \\=6[/tex]
Hence, Arc length of circle with circumference 18 and an arc with a 120° central angle is:
6
The measure of the length of the arc of circle with circumference 18 and has an arc with a 120 degree is 6 units.
What is the central angle of the arc?
Central angle is the angle which is substended by the arc of the circle at the center point of that circle. The formula which is used to calculate the central angle of the arc is given below.
[tex]\theta=\dfrac{s}{r}[/tex]
Here, (r) is the radius of the circle, (θ) is the central angle and (s) is the arc length.
A circle with circumference 18. As the circumference of the circle is 2π times the radius. Thus, the radius fo the circle is,
[tex]18=2\pi r\\r=\dfrac{9}{\pi}[/tex]
It has an arc with a 120 degree. Thus the value of length of the arc is,
[tex]120\times\dfrac{\pi}{180}=\dfrac{s}{\dfrac{9}{\pi}}\\s=6[/tex]
Hence, the measure of the length of the arc of circle with circumference 18 and has an arc with a 120 degree is 6 units.
Learn more about the central angle of the arc here;
https://brainly.com/question/4418954
