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

Question Illustration

Options

Option A

38.5 sq.cm.

Option B is correct

10.5 sq.cm.

Option C

18.5 sq.cm.

Option D

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.