+1348 The diagram shows eight congruent squares inside a circle. Every shaded square has one vertex on the circle. What is the ratio of the shaded area to the area of the circle? Express your answer as a decimal to the nearest hundredth.
+129895 Call the side of of one of the smaller shaded squares = 1
The total shaded area = 8(1^2) + 4 (pi) (1^2) / 4 = 8 + pi
The diameter of the circle = 1 + 1 + 2sqrt(2) = 2 +2 sqrt (2)
Then the radius = 1 + sqrt (2)
Area = pi ( 1 + sqrt (2))^2 = pi ( 3 + 2sqrt (2))
Ratio of shaded area / Area of circle = [ 8 + pi ] / [ pi ( 3 + 2sqrt (2)) ] ≈ .61
