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:
\(\[ C = 2\pi r \]\)
Where \(\( C \)\) is the circumference, \(\( \pi \)\) (pi) is a constant approximately equal to 3.14, and \(\( r \)\) is the radius of the circle.
Given that the circumference \(\( C \)\) is 31.4 miles, and using the value of \(\( \pi \)\) as 3.14, you can solve for \(\( r \)\) (radius) by rearranging the circumference formula to solve for \(\( r \)\) like so:
\(\[ r = \frac{C}{2\pi} \]\)
Now plug in the given values:
\(\[ r = \frac{31.4 \text{ miles}}{2 \cdot 3.14} \]\)
Divide 31.4 by \(\( 2 \times 3.14 \)\) to get the radius:
\(\[ r = \frac{31.4}{6.28} \]\)
When you calculate this, you'll get:
\(\[ r \approx 5 \]\)
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.
