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

$r = \frac{51.4}{2} = 25.7 \, \text{m}$

Step2: Obtener radio del círculo grande

$R = 49.1 \, \text{m}$

Step3: Calcular áreas de círculos

Área grande: $\pi R^2 = \pi (49.1)^2$, Área pequeña: $\pi r^2 = \pi (25.7)^2$

Step4: Área sombreada = Diferencia de áreas

$\text{Área} = \pi (R^2 - r^2) = \pi (49.1^2 - 25.7^2)$

Step5: Calcular $R^2 - r^2$

$49.1^2 = 2410.81$, $25.7^2 = 660.49$, $2410.81 - 660.49 = 1750.32$

Step6: Multiplicar por $\pi$ y redondear

$\text{Área} = \pi \times 1750.32 \approx 3.1416 \times 1750.32 \approx 5498.81$

Answer:

5498.81