Answer:-[tex]\text{The length of the radius of the circle=4.91 cm}[/tex]
Explanation:-
[tex]\text{Let r be the radius of the circle.}[/tex]
[tex]\text{Here, central angle}\theta=\frac{7\pi}{6}\\\text{Arc length\ l=18\ cm}[/tex]
[tex]\text{We know that }[/tex]
[tex]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}[/tex]
The radius of this circle is 4.9cm
To solve this problem, we need to first of all convert the angle from radians to degrees.
data;
[tex]7\pi /6 rads= 210^0[/tex]
The formula of length of an arc is given as
[tex]l_a_r_c=\frac{\theta}{360}*2\pi r[/tex]
Let's substitute the values and solve
[tex]18=\frac{210}{360}*2\pi r\\ 18=3.663r\\r=\frac{18}{3.663}\\r= 4.9cm[/tex]
From the calculations above, the radius of this circle is 4.9cm
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