Circles and squares
The radius of the circle is . It is inscribed in a square of side . The square, as well as circle, are divided into four equal portions by a horizontal and vertical line. Now arc in each smaller square was converted to four petals (shaded area) by taking a mirror image of them as shown in the diagram. What is the percent of the area of the petals to the total are of the big square?
Give your answer to the nearest integer.
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Here each of the small squares has an area (R^2). The area covered by circle in each square is [(pi)R^2]/4 So the empty area in the corner of the small square = (R^2) - [(pi)R^2]/4 = 0.215(R^2) In each square there are two such empty spaces, above and below the petal; so their total area = 0.43(R^2) So area of petal in each square = (R^2)- 0.43(R^2) = 0.57(R^2) So percent area of petal per small square or all the petals together in the big square(they are the same) = [0.57(R^2)/(R^2)] x 100 = 57%