Volume is the amount of space an objects takes up. This can be the amount of space a 3D shape occupies, or the space that a substance (solid, liquid or gas) fills. Capacity, on the other hand, is the amount a container can hold, rather than the amount of space the container itself displaces. Capacity will only be used in relation to a container and often involves liquids.
The units for volume are generally cubic units such as mm3, cm3 and m3. Capacity often deals with liquids therefore the common units are millilitres and litres.
Common units for volume from smallest to largest are:
Common units for capacity from smallest to largest are:
The symbol for litres can use a lower case or upper case letter L, but usually the upper case L is used to avoid confusion with the number $1$1.
Just as with lengths and areas to determine the correct unit to use, and be able to estimate the volume or capacity of an object it's useful to identify some common items that are about the size of the units above. Such as:
Sometimes we need to estimate the volume or capacity of an object and when estimating it is useful to have some points of reference. Consider the items above together with some other common items, such as those in the video below, as points for comparison in making estimates.
The following video shows some common items and units of capacity.
When referring to the capacity of a pool, which of the following could be an appropriate unit to use? Select all correct options.
mL
L
ML
Which of the following is it most appropriate to measure in cubic centimetres?
The area of a sheet of paper
The volume of air in a hall
The volume of an empty bottle
What is the best estimate for the capacity of the liquid in this container if it is able to hold $3600$3600 millilitres when full?
$2200$2200 millilitres
$1800$1800 millilitres
$1200$1200 millilitres
$3200$3200 millilitres
To convert units of volume we are converting cubic units, therefore we multiply or divide by the conversion factor for lengths cubed. This means we only have to remember the conversion factors for lengths.
When converting between units of volume:
Conversion factors for lengths:
Conversion factors for volume (the above factors are cubed).
Convert $5.85$5.85 m3 into cm3.
Think: Think about the steps needed to move from m3 to cm3. We are going from large units to small units, so we need to multiply. The conversion factor from m to cm is $100$100, therefore the conversion factor for m3 to cm3 is $100$1003 or $1000000$1000000
Do:
$5.85$5.85 m3 | $=$= | $5.85\times100\times100\times100$5.85×100×100×100 cm3 |
$=$= | $5.85\times1000000$5.85×1000000 cm3 | |
$=$= | $5850000$5850000 cm3 |
The following diagram shows the conversion factor between common units for capacity:
Note: The conversion factor is $1000$1000 at each step.
In some cases we may want to convert from units of volume to units of capacity, or vice-versa. For example, to find the capacity of a swimming pool, it would be easier to first measure the dimensions of the pool in metres and then convert to litres. In the diagram below we can see that $1$1 cm3 is equivalent to $1$1 mL and that $1$1 m3 is equivalent to $1000$1000 L.
A fish tank is $350000$350000 cm3. What volume of water in litres is required to fill the fish tank?
Think: Think about the steps needed to move from cm3 to litres. (cm3$\rightarrow$→mL$\rightarrow$→L). We know that $1$1 cm3 is equivalent to $1$1 mL, so first write the amount in mL and then convert to litres using the conversion factor or $1000$1000.
Do: First convert to millilitres: $350000$350000 cm3$=$=$350000$350000 mL
Now convert to litres: $350000$350000 mL$\div$÷$1000=350$1000=350 L
Convert $4920$4920 millilitres to litres.
$4920$4920 millilitres = $\editable{}$ litres.
Convert $6750$6750 cubic centimetres (cm3) to litres (L).
A small pond contains $3900$3900 L of water. What is the volume of the pond (in m3)?