SOLUTION: calculate the area of the shaded region enclosed by three identical circles tangent to each other. The radius of the circles is 5 inches

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Question 1199144: calculate the area of the shaded region enclosed by three identical circles tangent to each other. The radius of the circles is 5 inches
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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The centers of the circles form an equilateral triangle with the side a = 5+5 = 10 inches.


The area of this triangle is  A = a%5E2%2A%28sqrt%283%29%2F4%29 = 10%5E2%2Asqrt%283%29%2F4%29.


Each circular sector of interest has the area of  1%2F6  of the area of the circle of radius 10 inches.


So we need to subtract  3%2A%281%2F6%29%2Api%2Ar%5E2 = %281%2F2%29%2A3.14%2A%28sqrt%283%29%2F4%29 from A:


    the area of interest is  a%5E2%2A%28sqrt%283%29%2F4%29 - %281%2F2%29%2Api%2Ar%5E2  (exact formula).


Substitute the numbers and calculate using your calculator.

Solved.