Question

The circumference of a circle and the perimeter of a square are each 20 dm. Which has the greater area, the circle or the square? How much greater?

Answer 1

The formula for the circumference of a circle is $C = 2\pi R = 20,$ so $R =10/\pi,$ then the area is $S= \pi×100/\pi^2 = 100/\pi = 31.83 dm^2.$

The side of a square is 20/4 = 5 dm, so its area is $S = 5^2 = 25\,dm^2.$

So, the circle has a greater area. It is greater by 31.83 - 25 = 6.83 dm².