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Question

(B) When four circles of radius $r = 7\, cm$ are placed such that each touches two others,their centers form a square with side length $s = 2r = 14\,

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(B) When four circles of radius $r = 7\, cm$ are placed such that each touches two others,their centers form a square with side length $s = 2r = 14\, cm$.The area of this square is $s^2 = 14 	imes 14 = 196\, cm^2$.The space enclosed by the four pieces is the area of the square minus the area of the four quadrants of the circles lying inside the square.Each quadrant has an angle of $90^\circ$. The total area of the four quadrants is $4 	imes (\frac{90}{360} 	imes \pi r^2) = \pi r^2 = \frac{22}{7} 	imes 7 	imes 7 = 154\, cm^2$.Therefore,the required enclosed area is $196 - 154 = 42\, cm^2$.

Four circular cardboard pieces,each of radius $7\, cm$,are placed in such a way that each piece touches two other pieces. The area of the space enclosed by the four pieces is.......$cm^2$.

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