This experiment has been inspired by Matt Parker and his Stand Up Math channel.
As one of our Pi day activities, Simon attempted to calculate Pi by weighing a circle. In the video, you he first explains why this should work: the area of a circle with the radius r and the area of a square with a side of 2r can be expressed as Pi x r^2 and 4r^2 consecutively. This makes the ratio between the area of such a circle and the area of the square equal to Pi/4. In other words, Pi can be expressed as 4 times that ratio. But since both the circle and the square are made of the same material, their mass will also have the same ratio.
The result Simon got was pretty close, considering the low precision of our kitchen scales. As Simon’s math teacher correctly pointed out, the result would be much more precise if we had one thousand kids make their own circles and squares and weigh them, and then took the average of their outcomes.