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(D) The radius of the circle is $r = 4\, cm$.Area of the circle $= \pi r^2 = \pi 	imes (4)^2 = 16 \pi\, cm^2$.Since the square is inscribed in the ci

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$(16 \pi - 32)\, cm^2$

Vedclass · Answer

(D) The radius of the circle is $r = 4\, cm$.Area of the circle $= \pi r^2 = \pi 	imes (4)^2 = 16 \pi\, cm^2$.Since the square is inscribed in the circle,the diagonal of the square is equal to the diameter of the circle.Diameter of the circle $= 2 	imes r = 2 	imes 4 = 8\, cm$.Let the side of the square be $a$. The diagonal of a square is $a\sqrt{2}$.So,$a\sqrt{2} = 8$,which gives $a = \frac{8}{\sqrt{2}} = 4\sqrt{2}\, cm$.Area of the square $= a^2 = (4\sqrt{2})^2 = 16 	imes 2 = 32\, cm^2$.The area of the portion between the circle and the square is the difference between the area of the circle and the area of the square.Required area $= (16 \pi - 32)\, cm^2$.

$A$ square is inscribed in a circle whose radius is $4\, cm$. The area of the portion between the circle and the square is

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