The radius of a coin is 1, cm. If four of the | vedclass

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(D) Let the radius of each coin be $r = 1\, cm$.When four such coins are placed such that each touches the other two,their centers form a square with

Vedclass · Accepted Answer

$0.86$

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(D) Let the radius of each coin be $r = 1\, cm$.When four such coins are placed such that each touches the other two,their centers form a square with side length $s = 2r = 2\, cm$.The area of this square is $s^2 = (2)^2 = 4\, cm^2$.Inside this square,there are four sectors,each with a central angle of $90^\circ$ (since it is a square).The sum of the areas of these four sectors is $4 	imes (\frac{90}{360} 	imes \pi r^2) = \pi r^2 = \pi(1)^2 = \pi \approx 3.14\, cm^2$.The unoccupied space between the coins is the area of the square minus the area of the four sectors.Unoccupied space $= 4 - \pi = 4 - 3.14 = 0.86\, cm^2$.

The radius of a coin is $1\, cm$. If four of these coins are placed on a table so that the rim of each touches that of the other two,find the area of the unoccupied space between them. (in $cm^2$)

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