V is the total volume of the body, including the hollow space inside.
Let us consider a body of mass m and volume V. We can mathematically define the density of this body through the following relationship:
In the equation above, note that V is the total volume of the body, whether it is solid or hollow, as shown in the above figure of the volleyball. If the analyzed body is massive and homogeneous, such as, for example, a metal cube or a brick, the density can be called the specific mass – being represented by the Greek letter mi (µ) – of the material from which the body is made. .
In the International System of Units, the unit of specific mass or density is kg/m3, but the units g/cm3 and kg/L are often used. Therefore, we can write:
We cannot forget that, according to the studies of Thermology, the density of a substance varies with temperature, and in the case of gases it also varies with pressure.
Let us consider two materials, or bodies, A and B. We call the density of A with respect to B ( d AB ) as the quotient.
In the case of solid and liquid materials, we generally take as reference (B) water, at a temperature of 4°C. In the case of gases, we generally take oxygen as a reference, at 0°C and at sea level. According to the equation above, we can observe that the relative density has no unit, that is, the relative density is dimensionless.