Question

a search plane carries radar equipment that can detect metal objects (like submarine periscopes or plane wreckage) on the ocean surface up to 12.5 miles away. if the plane completes a circular flight pattern of 628 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 square miles. (round to the nearest hundred as needed.)

Explanation:

Step1: Find the radius of the circular flight - pattern

The formula for the circumference of a circle is $C = 2\pi r$. Given $C = 628$ miles and $\pi=3.14$, we can solve for $r$.
$r=\frac{C}{2\pi}=\frac{628}{2\times3.14}$
$r = 100$ miles.

Step2: Calculate the search - area

The search area is the area of a circle with radius $r + 12.5$ (since the radar can detect up to 12.5 miles away from the flight - path). The formula for the area of a circle is $A=\pi R^{2}$, where $R=r + 12.5$. Here, $R=100 + 12.5=112.5$ miles.
$A = 3.14\times(112.5)^{2}$
$A=3.14\times12656.25$
$A = 39740.625\approx39700$ square miles (rounded to the nearest hundred).

Answer:

39700