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)
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Question
Answer
SG_KP1
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