Question

both circles have the same center. what is the area of the shaded region? 19 yd r = 39 yd write your answer as a whole number or a decimal rounded to the nearest hundredth. square yards

Explanation:

Step1: Identify radii

Larger radius \( R = 39 \, \text{yd} \), smaller radius \( r = 39 - 19 = 20 \, \text{yd} \)

Step2: Calculate area difference

Shaded area \( A = \pi (R^2 - r^2) = \pi (39^2 - 20^2) \)

Step3: Compute and simplify

\( 39^2 - 20^2 = 1521 - 400 = 1121 \), so \( A = 1121\pi \approx 1121 \times 3.1416 \approx 3521.73 \)

Answer:

3521.73