Find the length of a side of a cube having a mass of 1.0 kg and the density of nuclear matter, taking this to be $2.3\times 10^{17}{\text{ kg/m}}^3$.

Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to calculate the side length of a cube that has a mass of 1.0 kilogram and has a density the same as that of nuclear matter so the density of a nucleus, which is 2.3 times 10 to the 17 kilograms per cubic meter. So density is mass divided by volume and the volume of a cube is the side length cubed so we substitute l cubed in place of V and then solve for l cubed by multiplying both sides by l cubed over ρ and then we have l cubed equals m over ρ and l then is m over ρ to the power of one-third so we raise both sides of this to the power of one-third and this is another way of taking the cube root of both sides so l is the cube root of mass divided by density. So that's 1.0 kilogram divided by 2.3 times 10 to the 17 kilograms per cubic meter all to the power of one-third and that is 1.6 micrometers.