Let us first define density as the amount of mass contained per unit volume of an object. It is technically a ratio, and is calculated using the formula:
So it is clear how we only need two components to calculate density: mass and volume. For a metal cube, we measure its mass by simply placing it on a mass balance. As for its volume, we’ll take advantage of the fact that a cube is regularly shaped - so just by measuring one side’s length with a ruler, all we then have to do is use the formula for the volume of a cube: V = l3. After that, it is simply a matter of dividing mass by volume!
The statue’s mass can be measured easily with a mass balance, the story is a little different for its volume, considering that it’s no longer regularly shaped - there’s no strict formula we can use! We do, however, have a different technique called the displacement method (or more interestingly, the Eureka method!) The steps are as follows:
- First, fill up a measuring cylinder approximately halfway and measure this initial volume (V1)
- Then, place the small statue inside, and measure the new volume (V2)
- Note that this new volume is simply the initial water volume combined with the statue’s own volume - therefore, volume of the statue is simply: Vs = V2 - V1
After that, just divide mass by volume, and we’ll have the statue’s density!