Sphere Packing

What is the length of the shortest pipe, of internal radius $50 mm$ , that can fully contain $21$ balls of radii $30 mm, 31 mm, \dots, 50 mm$ ?

Give your answer in micrometres ( $10^{- 6} m$ ) rounded to the nearest integer.

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.