Question

both circles have the same center. what is the area of the shaded region? d=51.4 m 49.1 m write your answer as a whole number or a decimal rounded to the nearest hundredth. square meters

Explanation:

Step1: Calcular radio del círculo pequeño

Radio pequeño \( r_{\text{peq}} = \frac{51.4}{2} = 25.7 \, \text{m} \)

Step2: Obtener radio del círculo grande

Radio grande \( r_{\text{grande}} = 49.1 \, \text{m} \)

Step3: Área sombreada = Área grande - Área pequeña

\( A = \pi (r_{\text{grande}}^2 - r_{\text{peq}}^2) \)

Step4: Calcular diferencia de cuadrados de radios

\( 49.1^2 - 25.7^2 = 2410.81 - 660.49 = 1750.32 \)

Step5: Multiplicar por π y redondear

\( A = \pi \times 1750.32 \approx 3.1416 \times 1750.32 \approx 5498.81 \)

Answer:

5498.81