Archimedes was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. He lived 2300 years ago.

Two of his numerous achievements were the approximation of number π ≈ 22/7 and the calculation of the area of a circle.

It was possible to measure the circumference of circle, for example, using a rope. It was more difficult to calculate the area of a circle. He invented a formula!

He separated a circle into many sectors and put them together. The picture shows a 12-sector split.

Increasing the number of separated sectors allowed him to find the formula of the area of a circle with the radius r.

What is the length W in the picture?