The Volume of Sphere

We have determined the length of the prehistoric measuring stick to be 523 millimeters. At that time, the metric unit was not used. If the metric unit was known, it meant that the largest sphere that could fit into a 1000 liter cube was 523 liters. The volume that the owner of the measuring stick determined from any cube by a factor of 0.523. Conversely, the volume of the largest sphere that can fit inside a cube by a factor of 1.913.

0.523 x ? = 523 (in any unit of measurement)

? / 1.913 = 0.523

Volume of the sphere                    V = (4 π x r³) / 3

                                                         V = 4 x π x 0.5³ / 3 m³

                                                         V = 0.523

                                                          (note 4 x π x 0.5³ = 1.57)