50.3k views
15 votes
PLEASE HELP

Both circles have the same center. The
circumference of the inner circle is
249.944 meters. What is the area of the
shaded region?

PLEASE HELP Both circles have the same center. The circumference of the inner circle-example-1

1 Answer

8 votes
Pretty much to find the area of the shaded region, you have to take the area of the smaller circle, and subtract it from the bigger circle.

First, to find the area of the smaller circle, you can use the circumference given to help you find that. Since the formula for Circumference is C=2rpi, you can solve for the radius by doing 249.944/(2*3.14).

The radius of the smaller circle will end up being 398/15 m as a fraction, and 26.53 rounded to the nearest hundredth.

Now since you have that, you can use the are of a circle formula to find the bigger and smaller circles.

A=pi(r)^2

For the smaller circle: 3.14*(26.53)^2
= 2210.06 meters squared

For the bigger circle: 3.14*(49+26.53)^2
= 17913.01 meters squared


Now subtract them:
17913.01-2210.06 = 15702.95

The area of the shaded is 15702.95
User Milen
by
7.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.