Verify that a $2.3\times 10^{17}\text{ kg}$ mass of water at normal density would make a cube 60 km on a side, as claimed in Example 31.1. (This mass at nuclear density would make a cube 1.0 m on a side.)

Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to verify that the side length of a cube containing 2.3 times 10 to the 17 kilograms of water is 61 kilometers. Now the density of the water is 1000 kilograms per cubic meter and density is mass divided by volume and for a cube, the volume will be the side length which we'll call d multiplied by itself three times and so we'll replace v with d cubed and then solve for d by multiplying both sides by d cubed over ρ, and then raise both sides to the power of one-third and so we have m over ρ to the power of one-third is going to be our side length. So that's 2.3 times 10 to the 17 kilograms divided by the density, all to the power one-third giving us 61 kilometers as our side length for cube.