Question

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

Answer 1

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