Question

a standard 1 kilogram weight is a cylinder 46.0 mm in height and 40.5 mm in diameter. what is the density of the material? kg/m³

Explanation:

Step1: Calculate the radius of the cylinder

The diameter $d = 40.5\ mm$, so the radius $r=\frac{d}{2}=\frac{40.5}{2}\ mm = 20.25\ mm=0.02025\ m$.

Step2: Calculate the volume of the cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$. The height $h = 46.0\ mm=0.046\ m$. Then $V=\pi\times(0.02025)^{2}\times0.046\ m^{3}\approx5.97\times 10^{-5}\ m^{3}$.

Step3: Calculate the density

The density formula is $
ho=\frac{m}{V}$. Given $m = 1\ kg$, so $
ho=\frac{1}{5.97\times 10^{-5}}\ kg/m^{3}\approx1.68\times 10^{4}\ kg/m^{3}$.

Answer:

$1.68\times 10^{4}$