To find the radius of a circle when you're given the circumference, you can use the formula that relates circumference and radius, which is:
[tex]\[ C = 2\pi r \][/tex]
Where [tex]\( C \)[/tex] is the circumference, [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14, and [tex]\( r \)[/tex] is the radius of the circle.
Given that the circumference [tex]\( C \)[/tex] is 31.4 miles, and using the value of [tex]\( \pi \)[/tex] as 3.14, you can solve for [tex]\( r \)[/tex] (radius) by rearranging the circumference formula to solve for [tex]\( r \)[/tex] like so:
[tex]\[ r = \frac{C}{2\pi} \][/tex]
Now plug in the given values:
[tex]\[ r = \frac{31.4 \text{ miles}}{2 \cdot 3.14} \][/tex]
Divide 31.4 by [tex]\( 2 \times 3.14 \)[/tex] to get the radius:
[tex]\[ r = \frac{31.4}{6.28} \][/tex]
When you calculate this, you'll get:
[tex]\[ r \approx 5 \][/tex]
To round the radius to the nearest hundredth, if necessary, you can check the third digit after the decimal point. In this case, there's no need because it's already a whole number.
Hence, the radius of the circle is approximately 5 miles.
