Question

A circle has a diameter of 5 meters and a square has a side length of 5 meters.

A. Which has the greater perimeter? how much greater?

B. Which has the greater area? how much greater?

Answer 1

For a square:

s = length of the side

P = 4s
A = s^2

For a circle:
C = pi*d
A = pi*r^2

Perimeter:

Square P = 4s = 4 * 5 m = 20 m

Circle: C = 3.14 * 5 m = 15.7 m

20 m - 15.7 m = 4.3 m

The perimeter of the square is 4.3 m greater than the perimeter of the circle.

Area:

Square: A = (5 m)^2 = 25 m^2

Circle: A = 3.14 * (2.5 m)^2 = 19.6 m^2

25 m^2 - 19.6 m^2 = 5.4 m^2

The area of the square is 5.4 m^2 greater than the are of the circle.