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.

Answer :

Given: Radius of cardboard = 7 cm


To find: Area of portion enclosed.


Explanation:



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


Thus,


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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