Nine circular designs are made in a square sh | vedclass

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(A) The radius of each circle is $r = 21\, cm$.Diameter of each circle is $d = 2r = 2 	imes 21 = 42\, cm$.Since there are $3$ circles along each side

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(A) The radius of each circle is $r = 21\, cm$.Diameter of each circle is $d = 2r = 2 	imes 21 = 42\, cm$.Since there are $3$ circles along each side of the square,the side length of the square is $S = 3 	imes d = 3 	imes 42 = 126\, cm$.Area of the square $ABCD = S^2 = 126^2 = 15876\, cm^2$.Area of one circle = $\pi r^2 = \frac{22}{7} 	imes 21 	imes 21 = 22 	imes 3 	imes 21 = 1386\, cm^2$.Area of $9$ circles = $9 	imes 1386 = 12474\, cm^2$.Area of the region without design = Area of square - Area of $9$ circles.Area = $15876 - 12474 = 3402\, cm^2$.

Nine circular designs are made in a square show-piece as shown in the diagram. If the radius of each circle is $21\, cm$,find the area of the region without design. (in $cm^2$)

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