What is Density and Volume?
Mass is a scalar quantity which is mostly dependent on the inertia. Inertia is the resistance of an object to change its state of motion whenever an external force is applied to it. Therefore, an object with greater mass has a high tendency to resist acceleration. The mass of an object helps to know how heavy the object is without gravity. It is constant because the mass remains the same at different places at a given moment. Density and volume are intrinsic characteristics of matters. In simple words, anything that has mass and occupies space also has volume and density. To understand the relationship between density and volume, one has to have a prior understanding of matter. Density can be said as the amount of mass present in a substance for a given volume. Density is the relationship between mass and volume. We can know from the density how tightly the molecules of an object are packed in the available space. The density of the object never changes with size and shape.
But the density can be changed depending on the temperature and pressure applied to the object which further results in the change in substance. Volume is a physical quantity that is derived from quantity and expresses the three dimensional extent of an object which is calculated using the SI unit. Example, the volume of a cube is equal to side times side times side. As the side of a square is the same, we can take the length of one side cube. Furthermore, an understanding of density and volume as general terms is also essential. Herein, volume is the physical space occupied in three dimensions by a matter, while density is the mass per unit of volume.
The volume of a substance is three dimensional. It is taken as length in three directions unlike area or length, and the volume of the substance.The standard unit used to measure volume is metre. The unit is converted into bigger and smaller units like a decimeter or kilometre based on how big or small the quantity is, it is done by simply dividing/ multiplying by tens, hundreds, thousands, and so on. The density of any object is defined as the mass of that object per unit volume. Density helps to determine how close or far away the molecules are packed in a given space. The very famous scientist known as Archimedes discovered the concept of the Density of an object. In the metric system, Density is measured in kg/m3 and is represented as D or ρ. The density of a substance does not change under some constant conditions without depending on the amount. Mass depends on the amount because we cannot define the mass of a substance without knowing its volume and other environmental conditions. There is a lot of difference between mass and density under different conditions and different elements and compounds. Hydrogen is the lightest atom and has one quarter the mass of helium which is the second lightest. Hydrogen atoms join together to form one molecule but one molecule of hydrogen weighs on half as much as one single helium atom. Due to the nature of the gas, some amount of hydrogen gas is about half of the density of helium gas under similar conditions. But, in solids and liquids the relationship of density is more complex. The atomic or molecular constituents come together and the density changes depending on the size and shape of the bond.
What is the Relation between Density and Volume?
The density and volume relation states that both are proportional to each other. It means that even a slight change in density is likely to cause a change in volume of that specific matter, be it an element or a compound.
Similarly, the reverse is also valid, wherein even a slight change in volume will lead to a change in density of a specific object. Alongside, you should also be familiar with the sign conventions for every parameter so as to represent the relationship in mathematical terms easily.
The mathematical expression for the relation between mass volume and density is given below -
⍴ = M/V
Where ⍴ (read rho) = density
M = mass, and
V = volume
Furthermore, as a student you should also note the units of both density and volume too. Consequently, as volume is a three-dimensional quantity, it has its unit in a cubic format, such as a cubic metre.
In the case of density, which is defined as the rate of change of mass per volume, the unit is kg/cubic metre and its likes. The unit for mass can be kilograms or grams, depending on SI and CGS units, whichever is applicable. Hence, students should be careful while establishing a relationship between mass volume and density and also while converting from one unit to another.
Most features are studied by the scientists. They may be measured in phases of 1 or greater of four properties: duration, time, mass, and electric powered charge. The quantity of a dice is a unit of duration cubed which means the duration can be increased by using width and then it is increased by using height. Volume is measured in terms of duration and it is described as the quantity of three dimensional area that an item occupies. Volume is measured in cubic metres, for example cubic centimetres. There are 1000 millilitres in one litre. Density is measured as the ratio of mass and density. Density is also taken as a quantity that tells the available space inside an area. The unit of density is g/cm3. Mass is difficult to find. Density is found in terms of mass and volume. Volume is stable and it is described as the space occupied by a substance. The size of the substance is different in different situations. The volume of a dice can be calculated by multiplying height and width. There are different ways of calculating volume of different objects.
Points to Remember
The relation between volume and density with mass has some key points that students should understand for explicit knowledge of the same. The points are listed below -
Any two matter having the same volume may not have the same density.
Any two matter having the same mass may not be equal in volume.
Water is an exception in this phenomenon, as it increases in volume while freezing, thereby having more volume in its solid state than that of its liquid state. This process begins at 4°C and is known as anomalous expansion of water.
Water is used as a reference for gauging density of other matters.
Cool air is denser than warm air.
While studying the relation between density volume and mass, students should note here that the density of water changes at different temperatures. Nonetheless, its density at 100 degrees Celsius is considered the basis of reference.
It would be best if you would also look into the conversion of density to volume and vice versa to develop an understanding of advanced numerical. Make sure you are able to convert them easily, for which you should memorise the basic formula for density.
For a piece of more detailed information on the mass volume and density and their related features, conversions and applications, go through our online learning programmes. They have the top-notch study materials drafted by our subject experts for your clarification.
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FAQs on Relation Between Density And Volume
1. What is the mathematical relationship between density and volume for any substance?
The density of a substance is defined as its mass per unit volume and is expressed as ρ = M / V, where ρ is density, M is mass, and V is volume. This shows that if mass remains unchanged, an increase in volume results in a decrease in density, and vice versa.
2. How does changing the volume of an object affect its density, assuming mass is constant?
If the volume increases while the mass stays the same, the density decreases. Similarly, reducing the volume while keeping mass constant makes the density higher, according to the formula ρ = M/V.
3. Why is the density of water considered as a standard for comparing densities of other materials in Physics?
Water's density at 4°C is used as a fundamental reference because it is easy to reproduce and acts as a baseline for defining the specific gravity and relative density of other substances. This helps standardise measurements in physics and chemistry, as per the CBSE 2025–26 syllabus.
4. Can two different substances with the same volume have different densities? Explain with an example.
Yes, two substances can have identical volumes but different densities if their masses differ. For example, a block of iron and a block of wood with the same volume will have different densities because iron is much heavier than wood for the same amount of space occupied.
5. How does temperature affect the density and volume relationship in liquids such as water?
As the temperature increases, most liquids including water expand, causing their volume to increase and density to decrease, if the mass remains constant. Notably, water behaves unusually near 4°C, expanding instead of contracting when cooled further, a phenomenon known as the anomalous expansion of water.
6. What is the correct SI unit for density and how is it derived from mass and volume?
The SI unit for density is kilogram per cubic metre (kg/m³), derived from mass (kg) divided by volume (m³). This reflects how much mass is present in one cubic metre of substance.
7. How can you calculate the mass of a substance when its density and volume are known?
To find the mass when density and volume are known, use the formula M = ρ × V. Multiply the density by the volume to get the mass in appropriate units.
8. Compare the density and volume of solids, liquids, and gases for the same mass. Why do differences occur?
- Solids: Highest density, smallest volume for a fixed mass as particles are closely packed.
- Liquids: Intermediate density and volume, particles are less tightly packed than solids.
- Gases: Lowest density, highest volume for the same mass because particles are far apart.
9. What are some common misconceptions students have about the relationship between density and volume?
A common misconception is that objects with larger volume must always have higher density. In reality, density depends on both mass and volume. Another misunderstanding is that changing the shape of an object changes its density; density remains constant for the same substance unless temperature or pressure is altered.
10. Why does ice float on water although both are made up of H2O molecules?
Ice floats on water because it has a lower density than liquid water. When water freezes, its molecules arrange in a way that increases the volume, resulting in decreased density. This is an example of the anomalous expansion of water and explains why icebergs stay afloat.
