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

Question

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.

Find the area of the shaded region.

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

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Answer 1 · 2018-04-10T08:24:45

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

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

#34.5575/3.1416=10.999968~=11# units

Hence radius of outer most circle is #11/2=5.5# units

Diameter of circle just smaller than this is #11-3=8# units i.e. its radius is #4# units and as area of a circle is #pir^2#, its area is

#pixx4^2=16pii#

Diameter of smallest circle is #8-2=6# units i.e. its radius is #3# units and its area is

#pixx3^2=9pii#

Hence areaof shaded region is #16pi-9pi=7pi#

or #7xx3.1416=21.9912# square units