In the figure, a circle of radius 2 cm is inscribed in a square. There are four smaller circles at each of the cornerof the square. Whatis the total area covered by all the five circles?
Explanation:
It has been given that radii OE = OF = 2 cm. Consequently, AB = 4 cm {side of the square}. AC = 4√2 cm
Further, let the radius of the smaller circles be r cm. Then, AP = r√2 cm. Thus, AQ = r√2 + r or r(√2 + 1) cm. There are two such regions on line AC. Hence, we can rewrite AC = 2 × r(√2 + 1) + 4. This is equal to 4√2 cm. On equating, we obtain r = (6 - 4√2) cm. We have been asked to find the total area covered by the five circles = 4π + 4 × π(6 - 4√2)2 cm2 Hence, Option A is the correct choice.