Question

both circles have the same center. the circumference of the inner circle is 160.768 miles. what is the area of the shaded region? write your answer as a whole number or a decimal rounded to the nearest hundredth. square miles

Explanation:

Step1: Calcular radio interno

$r_{inner} = \frac{C}{2\pi} = \frac{160.768}{2\times3.14} = 25.6\ \text{mi}$

Step2: Radio externo dado

$r_{outer} = 59\ \text{mi}$

Step3: Área de la región sombreada

$A = \pi(r_{outer}^2 - r_{inner}^2) = 3.14\times(59^2 - 25.6^2) = 3.14\times2825.64 = 8872.5096$

Answer:

8872.51