You have a copper cube that has a mass of 10 grams. If copper has a density of 8.96 `g/(cm^3),` what is the length of one side of the cube?

Hello!

By the definition, (average) density `rho` of a body is its mass `m` over its volume `V,`  `pho=m/V.`  For all objects made from the same homogeneous material this quantity is the same. It therefore considered as the density of this material (copper, as in our case).

Density and mass are given. Volume of a cube with the side of a length `d` is `V=d^3.` So  `rho=m/V=m/d^3`  and  `d^3=m/rho,`   thus  `d=root(3)(m/rho).`

In numbers it is `root(3)( (10g)/(8.96 (g)/(cm^3))) approx`  1.037 cm. This is the answer.