Question

The circumference of the inner circle is 270.04 miles. What is the area of the shaded region?

Answer 1

The answer is 5802.92mi^2

Answer 2

area of a circle = $\pi r^{2}$

circumference =$2\pi r$

Okay so the center of the circle is the same for both of the circles lets take that value as m so the radius of the inner circle is 54 - m

we have the circumference of the inner circle which is 270.04 we can find the value of m using that

$270.04=2\pi (54-m)\\270.04= 339.2-6.28m \\6.28m = 339.2-270.04\\m= 11.02$

the radius of the inner circle is therefore 42.98

and the full circle has a radius off 65.02

area of shaded region = area of full circle - area of inner circle

area of shaded region = $\pi (65.02)^{2} - \pi (42.98)^{2}$

area of shaded region = $13281.39 - 5803.4$

area of shaded region = 7478 rounded off to the nearest whole number