Question

A cube measures 2.0 cm on each edge and has a mass of 64.7 g. Calculate the density of the material that composes the cube. (The volume of a cube is equal to the edge length cubed.)

Answer 1

Hint: Density is the property of any substance that is characteristic to it which means that every substance has a unique density. It is defined as the mass per unit volume. For liquids, the density is given by dividing the mass of the liquid taken by the volume of the liquid taken. The SI units of density is $ kg/{m^3} $ . Density is commonly represented by the letter ‘D’ or the symbol $ \rho $ .

Complete Step By Step Answer:
The density of any material as described earlier is characteristic to every substance. Density is the measure of how much of the substance occupies a volume of 1 unit cube, at a fixed temperature and pressure. Specifically, it is the mass of the substance per unit volume.
Density is different for different materials, but is more commonly discussed among liquid substances. The formula for density can be given as:
 $ Density = \dfrac{{Mass}}{{Volume}} $
The unit of density is the same as that of mass divided by the units of volume. The common units to determine density is $ g/c{m^3} $ if it’s a solid and $ g/mL $ for liquids. It can also be given in terms of $ g/L $ .
The information given to us is: mass = 64.7g and the edge length = 2.0 cm
We are given a cube and the volume of the cube with edge length (a) can be given as: $ Volume = {a^3} $
Hence, the volume of the cube with edge length 2.0cm is $ volume = {(2)^3} = 8c{m^3} $
Now, we have the volume and mass, substituting the values in the density formula;
 $ Density = \dfrac{{64.7g}}{{8c{m^3}}} = 8.1g/c{m^3} $
Hence the density of the material that composes the cube is $ 8.1g/c{m^3} $ .

Note:
The relative density of an object will determine if a body will sink or float. If the density of the body is lower than that of water, it floats on the surface. And if the density is more than that of water, it will sink. There are two types of density, one is the relative density and one is the absolute density. Relative density is known as the specific gravity, which is the ratio of the density of a body with that of a reference material. Absolute density is the mass of the substance per unit volume expressed in $ g/c{m^3} $ .