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##