Using the length of an arc of a circle formula problem is solved. Then the length of the radius is 4.91 cm.
What is a circle?
It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Given
A circle has a central angle measuring [tex]\rm \dfrac{7 \pi}{6}[/tex].
And the length of an arc is 18 cm.
We know the arc formula.
[tex]\rm Length\ of \ arc = \dfrac{\theta}{2\pi} 2\pi *r[/tex]
Then the length of the radius will be
[tex]\rm 18 \ \ = \dfrac{\frac{7\pi}{6}}{2\pi} 2\pi *r\\\\\rm 18 \ \ = \dfrac{7 \pi}{ 6} *r\\\\108 \ = 7\pi *r\\\\r \ \ \ \ = \dfrac{108}{7 \pi}\\\\r \ \ \ \ = 4.91[/tex]
Thus, the length of the radius is 4.91 cm.
More about the circle link is given below.
https://brainly.com/question/11833983
