Volume and Capacity
Are volume and capacity the same thing? People may use them interchangeably but they are different, and the same. Let us explain!
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The volume of an object or substance is the amount of space it takes up. It is measured in cubic units as it is three-dimensional, i.e. it has length, width and height.
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This cube is a regular prism (see 3D Objects).
You can work out the volume of a regular prism, like a cube, by calculating the area of one layer (for example, the base) then multiplying by the number of other layers.
In this case the bottom layer is 10 rows of 10 cubes, or 10 x 10 = 100.
The cube is 10 layers high so we can work out the volume of this cube as 10 x 10 x 10 = 1000 cubic units.
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Objects with the same volume don't have to look the same.
For example, an object with the volume of 6 cubic units could be a rectangular prism with 2 layers of 3 cubes, or it could look like this formation of blocks.
Either way, it is taking up 6 cubic units of space.
Capacity is the amount a container can hold. Capacity is measured in fluid units - usually the metric units of millilitres, litres, kilolitres and megalitres.
You might think of a stadium being 'at capacity', indicating that all the seats are taken - the container (stadium) is full. This is a more general application of the word capacity but it can help you remember that capacity is about filling a container.
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This is where we have to start to think flexibly because capacity can also be referred to as internal volume.
We can use a can of drink to help us out.
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The can of drink below takes up space, therefore the can has volume.
The can also has a capacity - it can hold a certain amount of liquid when filled to the top.
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If we consider just this liquid, it also has volume - it is taking up space inside the can. There is a volume of liquid inside a container. So capacity is the internal volume of a container.
In the cans below, the volume of liquid in the can on the left is greater than the volume of liquid in the can on the right. Perhaps someone was thirsty!
If we focus just on the can on the left now, the total volume of this can - the amount of space it takes up - is very close to the volume of liquid inside it. Only the thin sheet of aluminium is the difference in these two measurements.
Displacement
When an object is fully submerged in a liquid it displaces its volume - the liquid moves around the object. The object must be submerged to calculate its volume.
For example, the marbles below are submerged and the water moves up because the marbles have displaced the water.
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It is interesting to know that a 1cm cube will displace 1mL of water.
So 1cm³ = 1mL and 1000cm³ = 1L.
This conversion is only true for water, not all liquids.
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Displacement is good for finding the volume of irregular objects.
You need to mark the volume of water before the object is submerged, and then after it is submerged. Then find the difference between the two markings.
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The story of Greek mathematician and engineer, Archimedes and his gold crown Eureka moment are a fascinating cultural context to investigate in relation to displacement. Such an exploration could include the popular children's book Mr Archimedes' Bath by Pamela Allen (Harper Collins, 1993).
