Question

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

Explanation:

Step1: Identify radii

Radio mayor \( R = 59 \, \text{yd} \), radio menor \( r = 33 \, \text{yd} \)

Step2: Área del círculo mayor

\( A_{\text{mayor}} = \pi R^2 = \pi (59)^2 = 3481\pi \, \text{yd}^2 \)

Step3: Área del círculo menor

\( A_{\text{menor}} = \pi r^2 = \pi (33)^2 = 1089\pi \, \text{yd}^2 \)

Step4: Área de la región sombreada

\( A_{\text{sombreada}} = A_{\text{mayor}} - A_{\text{menor}} = 3481\pi - 1089\pi = 2392\pi \)

Step5: Calcular valor numérico

\( 2392\pi \approx 2392 \times 3.1416 \approx 7514.69 \, \text{yd}^2 \)

Answer:

7514.69