Four circles of equal radius are drawn with centers, A, B, C and D such that ABCD is a square of side 14 cm and the circles touch externally as in the figure. The area of the shaded region bounded by the 4 circles is: (Take \(\pi=\frac{22}{7}\)).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 42 cm2
Each circle covers a quarter circle inside the square, because each angle of the square is \(90^\circ\). The four quarters make one full circle of radius 7 cm, half the side.
Area of the square \(=14\times14=196\,\mathrm{cm^2}\)
Area of four quarter circles \(\displaystyle =\frac{22}{7}\times7\times7=154\,\mathrm{cm^2}\)
Shaded area \(=196-154=42\,\mathrm{cm^2}\)