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?

Question

8868 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-01T19:31:12

#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#