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What is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters?

    ##1.931″m”^2##

    The formulas for the area of a circle with diameter ##d## and the area of a square with side length ##d## are;

    ##A_”circle” = pi r^2 = pi (d/2)^2 = pi/4 d^2##

    ##A_”square” = d^2##

    To find the difference, we can subtract the area of the circle from the area of the square.

    ##A_”square” – A_”circle”= d^2 – pi/4 d^2##

    ##= (1-pi/4)d^2##

    This is the general formula for the difference in the areas. Plugging in ##3″m”## for the diameter gives a value of;

    ##(1-pi/4)(3″m”)^2 = 1.931″m”^2##