How do I find the area of a shaded region within a circle?

The circumference of a circle is 34.5575 units. A smaller circle has a diameter that is 3 units smaller, and an even smaller circle has a diameter that is 5 units smaller than the largest circle. All three circles share point M.

enter image source here

Find the area of the shaded region.

Please explain too so I understand. Thank you so much for helping.

1 Answer
Apr 10, 2018

Area of shaded region is 21.9912 square units, say 22 square units.

Explanation:

Circumference of a circle is π times its diameter. As circumference of outer circle is 34.5575 units, considering π=3.1416, its diameter is

34.55753.1416=10.99996811 units

Hence radius of outer most circle is 112=5.5 units

Diameter of circle just smaller than this is 113=8 units i.e. its radius is 4 units and as area of a circle is πr2, its area is

π×42=16πi

Diameter of smallest circle is 82=6 units i.e. its radius is 3 units and its area is

π×32=9πi

Hence areaof shaded region is 16π9π=7π

or 7×3.1416=21.9912 square units