Question

a search plane carries radar equipment that can detect metal objects (like submarine periscopes or plane wreckage) on the ocean surface up to 13.5 miles away. if the plane completes a circular flight pattern of 1570 miles in circumference, how much area will it search? (use 3.14 as an approximation for π.) the flight pattern has a total search area of approximately (round to the nearest hundred as needed.)

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is $A = \pi r^{2}$, where $r$ is the radius of the circle. Here, the radius $r = 13.5$ miles.

Step2: Substitute the value of $r$ and $\pi$ into the formula

Substitute $\pi=3.14$ and $r = 13.5$ into the formula $A=\pi r^{2}$. So $A=3.14\times(13.5)^{2}$.
First, calculate $(13.5)^{2}=13.5\times13.5 = 182.25$.
Then, $A = 3.14\times182.25=572.265$.

Step3: Round the result

Round $572.265$ to the nearest hundred. Since the tens - digit is 7 which is greater than 5, we round up. So the result is 600.

Answer:

600 square miles