Volume is the amount of physical space a 3D object takes up. It is the 3D equivalent of area for a 2D shape. It is measured in cubic measurements, like cm³. It can be found by multiplying its length × height × width.
Measuring volume in this way is a basic equation and one of the first equations children learn about in school. Therefore, volume in Maths is essential, as it helps lay the foundations for further equations study.
What unit is volume measured in?
A cubic meter is the official volume unit recognized by The International System of Units. However, this unit is impractical because it designates a large volume, and smaller sizes are often needed. As such, it’s not used very often, especially in schools. Instead, people tend to measure volume in the:
- Cubic centimeters
- Cubic inches
- Milliliters
- Liters
- Gallons
All measurements for volume are cubic measurements. The cubic size is shown by a small 3. The volume is the product of three different heights multiplied together.
Formulas for the volume of common shapes
The formula for volume in Maths varies depending on which shape you are working with. Here are the formulas for finding the volume units of common 3D shapes:
- Cube volume = side³
- Cuboid (rectangular box) volume = length × width × height
- Sphere volume = (4/3) × π × radius³
- Cylinder volume = π × radius² × height
- Cone volume = (1/3) × π × radius² × height
- Pyramid volume = (1/3) × base area × height
Finding the volume of objects with different states of matter
Calculating volume in Maths can often depend on what shape you’re dealing with and what state you’re working with. Most often, children get taught about calculating the volume of a solid, but it’s also helpful to explore how best to calculate the volume of liquids and gases.
How to calculate the volume of a solid
When finding the volume units of standard, solid 3D shapes, you need the correct equation, and you’re set. However, things get a little trickier when you want to find the volume of irregular shapes.
There is no set equation to follow to find the volume of an irregular shape. However, all hope is not lost, as there are slightly unorthodox ways to work out the volume. For instance, you can try Archimedes’ Gold Crown method. This method was born when the famous mathematician, Archimedes, was tasked with determining whether the King’s (Hiero) crown was made from pure gold or just gold-plated. The trick was that Archimedes could not destroy the crown in the process. So Archimedes got to work. One day, the idea came to him when he was having a bath. Archimedes stepped into the bathtub and noticed that the water level rose as he entered it. From this observation, Archimedes concluded that the volume of water displaced must be equal to the volume of the part of his body he had submerged. Knowing the King’s crown’s volume and weight, he could work out the density and then compare it with the density of pure gold. In doing so, Archimedes was able to work out whether the King’s crown was made of pure gold or not.
While working with very different objects and circumstances, you can use Archimedes’ Gold Crown method to find the volume of any irregular shapes you encounter.
Here are the steps you must take to follow Archimedes’ Gold Crown method:
- Get a larger container than the object you want to measure the volume of. It can be anything that holds water, such as a basin, a bucket, a measuring cup, or a beaker. Ensure the container has a scale.
- Pour water into the container that you have chosen and use the scale to read the volume measurement.
- Place your object inside the container of water. Ensure the thing is completely submerged so that you can measure its whole volume
- Use the scale to read the volume.
- Compare the two volumes; the difference between the measurements is the volume of your object.
How to calculate the volume of a liquid
It is pretty simple to measure the volume of a liquid; all you need is a container with a scale of measurement on it. Some of the containers that scientists use to measure the volume of liquids are:
- Beakers
- Flasks
- Burettes
- Pipettes
- Graduated cylinders
You can then pour the liquid into the container, ensuring that it’s placed on a flat surface and that the liquid is the only thing filling the container. Then, take a reading off the side, where the liquid stops against the measurements. It will be the volume of the liquid.
How to calculate the volume of a gas
Things are a little more complicated when measuring the volume of gas. There are many reasons why this is the case, one of which is that the volume of gas is heavily influenced by temperature and pressure. Moreover, gases expand to fill any container that they are in
There are some methods you can use to try and measure the volume of gas, however. For example, you can use the balloon method. This method involves inflating a balloon with the gas that you are trying to measure the volume of. Then, you can use Archimedes’ Gold Crown method, which is detailed above. Place the balloon into a container of water, and check the difference in volume before and after the balloon is placed.
In chemistry, a syringe is used to measure the volume of gas. This gas syringe is used to insert or withdraw a volume of gas from a closed system.
There is also an equation for calculating the volume of gas. All you must use in the equation is the density and mass of the gas whose volume you are trying to measure. The equation is:
Volume = mass/density
