Answer: The area of the shaded region is 150.72 km^2
Step-by-step explanation: The first bit of information we have is that both the inner circle and the outer circle have the same center. The radius of the inner circle can be calculated since we have been given the circumference (25.12) and the value of pi (3.14). The circumference of a circle is given as
Circumference = 2 x Pi x radius
With the values available, we now have
25.12 = 2 x 3.14 x radius
25.12 = 6.28 x radius
Divide both sides of the equation by 6.28
radius = 4
Having calculated the radius of the inner circle, the area now becomes;
Area = Pi x radius^2
Area = 3.14 x 4^2
Area = 3.14 x 16
Area = 50.24 km^2
The radius of the outer circle is the addition of 4 (on the shaded region) to the radius of the inner circle and that gives us 8.
Next we calculate the area of the outer circle which is
Area = Pi x radius^2
Area = 3.14 x 8^2
Area = 3.14 x 64
Area = 200.96 km^2
Now that we have determined the area of both the inner circle and the outer circle, the area of the shaded region is simply the difference between both of them, that is
Area of shaded region = 200.96 - 50.24
= 150.72 km^2
