Density is mass/volume, that is, how much matter is there in a given amount of space. Since we are given the mass and density we can then solve for the volume, then use the volume to find the dimensions. So if we use the equation density = mass/volume and solve for volume, that gives volume = mass/density using a little algebra (since we can divide both sides by the mass, then multiply both sides by volume). Thus we take our mass (45.85g) and divide it by the density (19.3 g/cm3) which gives us 2.38 to the nearest hundredth. This is the total volume so we aren’t done! We need to get the cube root so we can have the side length of the perfect cube, since all the side lengths are equal. The cube root of 2.38 is 1.34 rounded, and our final answer is 1.34cm.
If I was taking a test and saw this and had no idea or didn’t remember I could use the units given as a hint (again density is in g/cm3) or perform different operations with the two values given until I get close but you would still have to understand that we are not looking for a total volume of a cube, but the side lengths!
