The standard kilogram is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material?

Density is mass per unit of volume, usually measured in g/cm³. So first determine the volume of the cylinder:

v = π r ² h = π ((39.0 mm) / 2)² (39.0 mm)

v = 59,319/4 π mm³ ≈ 46,589 mm³ ≈ 46.589 cm³

Then the density is

ρ = m / v

ρ = (1 kg) / v = (1000 g) / v

ρ ≈ 21.464 g/cm³

Or, if you want to preserve the given units, that's

ρ ≈ 0.00002146 kg/mm³

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h o h o hope you have a merry christmas!