**Problem Description**A search plane carries radar equipment that can detect metal objects (like submarine periscopes or plane wreckage) on the ocean surface up to 15.5 miles away. If the plane completes a circular flight pattern of 471 miles in circumference, how much area will it search? (Use 3.14 as an approximation for π.)**Question**The flight pattern has a total search area of approximately _____ square miles. (Round to the nearest hundred as needed.)**Diagram Explanation**The image includes a map with a search area depicted as a circle centered between Madagascar, India, and Saudi Arabia in the Indian Ocean. The circle represents the circular flight pattern of the search plane.**Solution Approach**1. **Determine the Radius**: Use the circumference formula \( C = 2\pi r \) to find the radius \( r \). - Given \( C = 471 \) miles - Use \( \pi \approx 3.14 \) \[ r = \frac{C}{2\pi} = \frac{471}{2 \times 3.14} \approx 75 \text{ miles} \]2. **Calculate the Area**: Use the formula for the area \( A = \pi r^2 \). \[ A = 3.14 \times (75)^2 = 3.14 \times 5625 \approx 17,662.5 \text{ square miles} \]3. **Round the Area**: - Rounded to the nearest hundred: \( 17,700 \) square milesTherefore, the total search area is approximately **17,700 square miles**.

The search plane radar equipment can detect objects 15.5 miles away. The plane covers a circular pattern 471 miles in circumference. Obtain the radius: 23.14r=471r≈75 The area searched by the plane is obtained as follows: Within the circle, radar equipment can detect objects 15.5 miles away. Hence, the inner radius is 75-15.5=59.5 miles. Outside the circle, radar equipment can detect objects 15.5 miles away. Hence, the outer radius is 75+15.5=90.5 miles.The area searched by the plane is region bounded within these two circles of radii 59.5 and 90.5. Hence, we have 3.1490.52-59.52≈14,601 Therefore, the area searched by the plane is 14,600 sq miles.