Geometry-2 (FMS-2009)

Let each side of a square is 20 cm. Four equal circles, each of radius 10 cm are drawn about the four corners of the square so that each touches two of the others. Find the area enclosed between the circumferences of the circles?

(1)86 sq.cm  (2)314 sq.cm    (3)78 sq.cm        (4)none of these

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Solution:

Given that radius of circle = 10 cm;           Length of side of square = 20 cm;

Area of the shaded region = Area of the square – 4(Area of each quarter circle)

                                                = (20²) – 4(π*10²/4)

                                                = 400 – (3.14*100) = 400 – 314 = 86

Answer (1)