The standard kilogram (fig. 1.1a) is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. what is the density of the material?

The volume of a cylinder is calculated as pi*h*d^2/4, so in this case, V = pi * (39 mm) (39 mm) ^2 / 4 = 46,589 mm^3. Dividing the mass of 1 kg by the volume of 46,589 mm^3 gives a value of 2.1464 x 10^-5 kg/mm^3. Usually, density values are given in kg/m^3, so we can convert by multiplying by 1x10^9, which gives a value of 21,464 kg/m^3.