Question

both circles have the same center. the circumference of the inner circle is 326.56 millimeters. what is the area of the shaded region? diagram: two concentric circles (inner white, outer yellow shaded), dashed line labeled 22 mm, inner circle labeled c=326.56 mm write your answer as a whole number or a decimal rounded to the nearest hundredth. square millimeters

Explanation:

Step1: Encontrar radio interno

Usando \( C = 2\pi r \), \( r_{\text{inner}} = \frac{326.56}{2 \times 3.14} = 52 \, \text{mm} \)

Step2: Calcular radio externo

\( r_{\text{outer}} = 52 + 22 = 74 \, \text{mm} \)

Step3: Área del anillo

\( \text{Área} = \pi (74^2 - 52^2) = 3.14 \times (5476 - 2704) = 3.14 \times 2772 = 8704.08 \, \text{mm}^2 \)

Answer:

8704.08