Question

A circle has a central angle measuring 7pi/6 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

Answer:-$\text{The length of the radius of the circle=4.91 cm}$

Explanation:-

$\text{Let r be the radius of the circle.}$

$\text{Here, central angle}\theta=\frac{7\pi}{6}\\\text{Arc length\ l=18\ cm}$

$\text{We know that }$

$l=r\theta\\\Rightarrow18=r(\frac{7\pi}{6})\\\\\Rightarrow\ r=\frac{18\times6}{7\pi}\\\\\Rightarrow\ r=\frac{108}{7\times3.14}\\\\\Rightarrow\ r=\frac{108}{21.98}\\\\\Rightarrow\ r=4.91\approx4.9\ cm\\\text{Therefore, the length of the radius of the circle=4.91 cm}$

Answer 2

Α * R = L where L is the length of the arc of the circle, R is the radius of the circle, and α is the central angle measured in radians, so:

$\cfrac{7 \pi }{6}* R =18 \\ \\ 7*3.14* R=18*6 \\ \\ 21.98 R=108 \\ \\ R=108/21.98 \approx4.9 \ \text{cm}$