A square and a circle have the same perimeter. Find the ratio of the area of the square to the area of the circle.

Guest May 16, 2020

#1**+2 **

Since we are finding a ratio, we can choose whatever we want to be the perimeter of the square.

I'm going to choose 40; this makes each side of the square equal to 10 and the area equal to 100.

Since the circle has the same perimeter (circumference), I'm going to use the formula for the circumference of the circle to find the radius of the circle.

C = 2·pi·r ---> 40 = 2·pi·r ---> 40 / (2·pi) = r ---> r = 6.366 (approximately)

The area of the circle is: pi·r^{2} = pi·6.366^{2} = 127.3 (approximately)

The ratio of the area of the square to the area of the circle is: 100 / 127.3 = 0.786 (approximately)

geno3141 May 16, 2020

#2**+1 **

Thx, geno......here's another way

Call the perimeter of the circle 2pi * r

Then the side of the square must be [ 2pi * r] / 4 = [ pi * r ] 2

Then the area of the square = pi^2 r^2 / 4

And the area of the circle is pi * r^2

So....the ratio of the area of the square to the area of the circle is :

pi^2 * r^2 / 4 pi

___________ = _____ ≈ .785

pi * r^2 4

CPhill May 16, 2020