In Archimedes' day, close approximations of pi had been known for over 1,000 years. An Egyptian document dated to 1650 B.C., for example, gives a value of 4 (8/9) 2, or 3.1605. Archimedes' value ...

the area of both circular faces is 2 × π × 5² = 50π m². When using the approximation π = 3۰142, the area of both circular faces is 2 × 3۰142 × 5² = 157۰1 m². Image caption ...