A square of side-length 30 cm is divided into nine smaller identical squares. The large square contains three circles with radii 5 cm (bottom right), 4 cm (top left) and 3 cm (top right), as shown. What is the total area of the shaded part?
A 400 cm2 B. 500 cm2 C. (400 + 50π) cm2 D. (500 − 25π) cm2 E. (500 + 25π) cm2
B.
The sum of the areas of the two smaller grey circles is the same as that of the white circle since (3π)2 + (4π)2 = (5π)2. This means that the shaded area is the same as the area of the five of the smaller squares. Each of the smaller squares has and area of 10 cm × 10 cm = 100 m2. The shaded area is then 5 × 100 cm2 = 500 cm2
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