Question

both circles have the same center. what is the area of the shaded region? 41 in r=20 in write your answer as a whole number or a decimal rounded to the nearest hundredth. square inches submit

Explanation:

Step1: Radio mayor del círculo

$R = 41 \, \text{in}$

Step2: Radio menor del círculo

$r = 20 \, \text{in}$

Step3: Área del círculo mayor

$A_{\text{mayor}} = \pi R^2 = \pi (41)^2 = 1681\pi$

Step4: Área del círculo menor

$A_{\text{menor}} = \pi r^2 = \pi (20)^2 = 400\pi$

Step5: Área de la región sombreada

$A_{\text{sombreada}} = A_{\text{mayor}} - A_{\text{menor}} = 1681\pi - 400\pi = 1281\pi$

Step6: Calcular el valor numérico

$A_{\text{sombreada}} \approx 1281 \times 3.1416 \approx 4024.39$

Answer:

4024.39