A rectangular sheet of cardboard is of 4 , cm | vedclass

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(C) The area of the rectangular sheet is given by $Area_{rect} = length 	imes width = 4 \, cm 	imes 2 \, cm = 8 \, cm^{2}$.To cut a circle of the gr

Vedclass · Accepted Answer

$(8-\pi) \, cm^{2}$

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(C) The area of the rectangular sheet is given by $Area_{rect} = length 	imes width = 4 \, cm 	imes 2 \, cm = 8 \, cm^{2}$.To cut a circle of the greatest possible area from a rectangle,the diameter of the circle must be equal to the smaller side of the rectangle.Here,the smaller side is $2 \, cm$,so the diameter $d = 2 \, cm$,which means the radius $r = 1 \, cm$.The area of this circle is $Area_{circle} = \pi r^{2} = \pi 	imes (1)^{2} = \pi \, cm^{2}$.The area of the remaining portion is the difference between the area of the rectangle and the area of the circle.$Area_{remaining} = Area_{rect} - Area_{circle} = 8 - \pi \, cm^{2}$.

$A$ rectangular sheet of cardboard is of $4 \, cm \times 2 \, cm$. If a circle of the greatest possible area is cut from it,then the area of the remaining portion is:

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