Question

A circle has a central angle measuring StartFraction 7 pi Over 6 EndFraction radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3. 14 for Pi. 3. 7 cm 4. 9 cm 14. 3 cm 15. 4 cm.

Answer 1

The radius of the circle is 4.91 cm.

Circle

It is a special kind of ellipse whose eccentricity is zero and foci are coincident with each other. 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

The arc of the circle is 18 cm.

And the angle is 7π/6.

To find

The radius of the circle.

How to get the radius of the circle?

Let r be the radius of the circle.

We know the arc formula of the circle

$\rm Arc = \dfrac{angle}{\pi} \pi r$

We know the arc is 18 and the angle is 7π/6. then

$\begin{aligned} \rm Arc &= \rm \dfrac{angle}{\pi} \pi r\\\\18 &= \rm \dfrac{7\pi}{6}*r\\\\\dfrac{108}{7\pi} &= \rm r\\\\\rm r &= 4.91 \end{aligned}$

Thus, the radius of the circle is 4.91 cm.

More about the circle link is given below.

https://brainly.com/question/11833983