Question

both circles have the same center. what is the area of the shaded region? 15 mi r = 40.6 mi write your answer as a whole number or a decimal rounded to the nearest hundredth. square miles

Explanation:

Step1: Encontrar radio exterior

$R = 40.6 + 15 = 55.6\ \text{mi}$

Step2: Calcular área anillo

$Área = \pi(R^2 - r^2) = \pi(55.6^2 - 40.6^2)$

Step3: Computar diferencia de cuadrados

$55.6^2 - 40.6^2 = (55.6 - 40.6)(55.6 + 40.6) = 15 \times 96.2 = 1443$

Step4: Calcular área final

$Área = \pi \times 1443 \approx 3.1416 \times 1443 \approx 4533.33$

Answer:

4533.33 square miles