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Question

Four identical circles that touch one another lie inside a square as shown. What fraction of the square is not covered by the circles? (Take pi=22/7)

Answer

Answer = 3/14

#1.  Area of Circle = πr2, Area of 4 circles = 4πr2 

#2.  Area of Square:

a) Side of square = 4r

b) Area of square = (4r)2 or 16r2

#3.  Area Shaded by Circle:

a) 4πr2 / 16r2

b) cancel r2 , 4π / 16 or [ 4 * (22/7) ] / 16 –> (88/7) / 16 –> 88/7 x 1/16 –> 88 / 112

c) simplify = 11/14

#4.  Unshaded area = 1 – Shaded area, or 1 – 11/14 = 3/14

 

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