SOLUTION: In the figure above, the circle has center Y and the four shaded semicircles each have area 18π. What is the circumference of the circle? image: http://152.46.13.240/MoodleCo

Algebra ->  Circles -> SOLUTION: In the figure above, the circle has center Y and the four shaded semicircles each have area 18π. What is the circumference of the circle? image: http://152.46.13.240/MoodleCo      Log On


   

Question 913729: In the figure above, the circle has center Y and the four shaded semicircles each have area 18π. What is the circumference of the circle?
image: http://152.46.13.240/MoodleContent/SATprep/Math%20Unit%207/Lesson%203%20Assignment/cb4.gif

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
r= radius of the small semicircles; R=4r= radius of the ;arge circle.
4%2A%281%2F2%29%2Api%2Ar%5E2=18pi= total area of the 4 semi-circles.
2pi%2Ar%5E2=18pi= total area of the 4 semi-circles.
r%5E2=18pi%2F2pi--->r%5E2=9--->r=3
So, R=4r=4%2A3=12

Circumference of the circle =2pi%2AR=2pi%2A12=highlight%2824pi%29