## Sunday, August 16, 2020

### [iqztvkvf] Cube root of density

5 pounds is a weight people can probably relate to, perhaps as a dumbbell weight.  Or half gallon + 1.5 cup + 4 teaspoon of water.  Or 5 pint - 6 tablespoon - 2 teaspoon ("pint is a pound").

We calculate the diameters of spheres of various materials that weigh 5 lb.

water 1 g/cc 6.4176889 inch

glass (fused quartz) 2.2 g/cc 4.9344388 inch

aluminum 2.70 g/cc 4.6088305 inch

iron 7.874 g/cc 3.2258699 inch

depleted uranium 19.05 g/cc 2.4029625 inch

gold 19.32 g/cc 2.391716 inch

tungsten 19.35 g/cc 2.3904794 inch

iridium 22.4 g/cc 2.2766485 inch

Example input to 'units' program for iridium: (5 lb / (22.4 g / cc) / (4|3) / pi) ^ (1|3) * 2

Bogusly too many significant figures, of course.  Round appropriately, probably based on the purity of your material and what your machining tools can do.

Subjectively, linear dimension does not decrease very much after lead because of the cube root.

Metric version:

2 kg is a weight people can probably relate to, e.g., 2 L of water.  We calculate the diameters of spheres of various materials that weigh 2 kg.

water 1 g/cc 15.631853 cm

glass (fused quartz) 2.2 g/cc 12.019034 cm

aluminum 2.70 g/cc 11.225935 cm

iron 7.874 g/cc 7.8573962 cm