This exercise involves the formula for the area of a circular sector. The area of a sector of a circle with a central angle of $5 \pi / 13 \mathrm{rad}$ is $18 \mathrm{~m}^{2}$. Find the radius of the circle. (Round your answer to one decimal place.) $\mathrm{m}$ Need Hetp? Read it Watch it

Step 1 ：This exercise involves the formula for the area of a circular sector.

Step 2 ：The area of a sector of a circle with a central angle of \(5 \pi / 13 \mathrm{rad}\) is \(18 \mathrm{~m}^{2}\). We are asked to find the radius of the circle.

Step 3 ：We can now substitute the given values into the formula to find the radius. We have \(A = 18 m^2\) and \(\theta = 5\pi/13 rad\). So, \(r = \sqrt{\frac{2*18}{5\pi/13}}\).

Step 4 ：Substituting the values, we get \(r = \sqrt{\frac{2*18}{1.2083048667653051}}\).

Step 5 ：Solving the above expression, we get \(r = 5.5\).

Step 6 ：Final Answer: The radius of the circle is \(\boxed{5.5}\) m.