Question

both circles have the same center. the circumference of the inner circle is 244.92 miles. what is the area of the shaded region? image of concentric circles, inner circle labeled c=244.92 mi, dashed line labeled 20 mi write your answer as a whole number or a decimal rounded to the nearest hundredth. square miles submit

Explanation:

Step1: Find inner radius

Given inner circumference \( C = 244.92 \) mi, \( C = 2\pi r \). So \( r = \frac{C}{2\pi} = \frac{244.92}{2\times3.14} = 39 \) mi.

Step2: Determine outer radius

The 20 mi is the width, so outer radius \( R = r + 20 = 39 + 20 = 59 \) mi.

Step3: Calculate shaded area

Shaded area = \( \pi R^2 - \pi r^2 = \pi (R^2 - r^2) = 3.14\times(59^2 - 39^2) = 3.14\times1960 = 6154.4 \) sq mi.

Answer:

6154.4