In the adjoining figure radius of each circle is 3.5 cm. Find the area of the shaded portion.

Options
38.5 sq.cm.
10.5 sq.cm.
18.5 sq.cm.
18.2 sq.cm.
Explanation
The four circles are arranged such that their centers form a square. The side length of this square is 2 times the radius of a circle. Given radius (r) = 3.5 cm. Side of the square formed by centers = 2 * 3.5 = 7 cm. Area of this square = side^2 = 7^2 = 49 sq.cm. The shaded portion is the area of this square minus the area of four quadrants (one from each circle) that lie within this square. Area of four quadrants = 4 * (1/4) * π * r^2 = π * r^2. Area of four quadrants = (22/7) * (3.5)^2 = (22/7) * (7/2)^2 = (22/7) * (49/4) = (22 * 7) / 4 = 11 * 7 / 2 = 77 / 2 = 38.5 sq.cm. Area of shaded portion = Area of square - Area of four quadrants = 49 - 38.5 = 10.5 sq.cm.