A landscaper plants circular flowerbeds in square plots of various sizes. After

Question

A landscaper plants circular flowerbeds in square plots of various sizes. After planting fowers (shaded region shown), grass is put down to form a lawn in the (white regions). remaining arca of the square Complete the followving table. Side length of Area of circular Area of grass in square feet, G Radius of circular Area of square plot square plot in eet,flowerbed in feet,in square feet, P flowerbed in square feet, Preview Preview Preview Preview Preview Preview Preview Preview Preview Preview Preview Preview Preview Preview 0.2 3.5

Explanation / Answer

x=2r

=>r=(x/2)

P=x2, F=r2=(x/2)2=(/4)x2,G=P-F=x2 - (/4)x2=((4-)/4)x2

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x r P F G 1 0.5 1 (/4)= 0.78534 ((4-)/4)=0.2146 0.2 0.1 0.04 (/4)*0.04=0.01=  0.031416 ((4-)/4)*0.04=0.01(4-)=0.008584 3.5 1.75 12.25 (/4)*12.25= 3.0625= 9.6211275 ((4-)/4)*12.25=3.0625(4-) =2.62887 6 3 36 (/4)*36=9= 28.274 ((4-)/4)*36=9(4-)=7.725666

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