Answer:
The radius of the circle is 12 inches.
Step-by-step explanation:
Given:
The radius of a circle in which a 30° arc is 2π.
Now, we put the formula of circumference first.
[tex]C=2\pi r[/tex]
Now, since 30 is one twelfth of 360, a 30° arc will be one twelfth of the whole circumference. So, if you call the arc length A, you have:
[tex]A=\frac{C}{12}=\frac{2\pi r}{12}=\frac{\pi r}{6}[/tex]
So, we know the arc length, now we can put the value and solve the following equation:
[tex]\frac{\pi r}{6}=2\pi[/tex]
Multiplying both sides by 6 and then dividing both sides by π we get :
[tex]r=12[/tex].
Therefore, the radius of the circle is 12 inches.
