The radius of the circle is 7.5 m
From the question,
We are to determine the value of the radius of the circle
Using the formula
[tex]l = \frac{\theta}{360 ^\circ} \times 2\pi r[/tex]
Where
[tex]l[/tex] is the length of arc
θ is the angle subtended
and r is the radius
From the given information,
[tex]l = 3\pi \ m[/tex]
[tex]\theta = 72^\circ[/tex]
Putting the parameters into the equation, we get
[tex]3\pi = \frac{72^\circ}{360^\circ}\times 2\pi r[/tex]
This becomes
[tex]3 = \frac{1}{5}\times 2r[/tex]
Therefore,
[tex]2r = 15[/tex]
[tex]r = \frac{15}{2}[/tex]
[tex]r = 7.5 \ m[/tex]
Hence, the radius of the circle is 7.5 m
Learn more on arc of a circle here: https://brainly.com/question/4174930
