Q. 185.0( 2 Votes )
Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.
Given: Radius of cardboard = 7 cm
To find: Area of portion enclosed.
The four circles are placed in such a way that each piece touches the other two pieces.
So, by joining the centers of the circles by a line segment, we get a square ABDC with sides as,
AB = BD = DC = CA = 2(Radius) = 2(7) cm = 14 cm
Now, Area of the square = (Side)2 = (14)2 = 196 cm2
Since, ABDC is a square, ∴ each angle has a measure of 90°.
∴ ∠ A = ∠ B = ∠ D = ∠ C = 90° = π/2 radians = θ (say)
Also, Radius of each sector = 7 cm
Area of the sector with central angle A = (1/2)r2θ
Since the central angles and the radius of each sector are same, therefore area of each sector is 77/2 cm2
∴ Area of the shaded portion = Area of square – Area of the four sectors
= 196 – 154
= 42 cm2
Hence, required area of the portion enclosed between these pieces is 42 cm2.
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