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 mm^{3}, cm^{3} and m^{3} but we can also use units such as millilitres and litres to describe volumes. Capacity uses the units for volume and given it often deals with liquids 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 volume of 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
The following diagram shows the conversion factor between different units of volume.
The conversion factors for volume involve very large numbers, so index notation is used in this conversion chart. $10^3=1000$103=1000, or "$1$1 followed by $3$3 zeros".
However, rather than remembering these factors it is useful to understand that to convert units of volume we are converting the three length dimensions of a cube unit. We can do this by multiplying or dividing by the conversion factor for lengths three times - that is multiply or divide by the conversion factor cubed. This means we only have to recall the conversion factor for lengths.
When converting between units of volume:
Convert $5.85$5.85 m^{3} into cm^{3}.
Think: Think about the steps needed to move from m^{3} to cm^{3}. We are going from large units to small units, so we need to multiply. The conversion factor from m^{3} to cm^{3} is $1000000$1000000, which can be remembered as multiplying by conversion from metres to centimetres three times.
Do:
$5.85$5.85 m^{3} | $=$= | $5.85\times100\times100\times100$5.85×100×100×100 cm^{3} |
$=$= | $5.85\times1000000$5.85×1000000 cm^{3} | |
$=$= | $5850000$5850000 cm^{3} |
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 cm^{3} is equivalent to $1$1 mL and that $1$1 m^{3} is equivalent to $1000$1000 L.
A fish tank is $350000$350000 cm^{3}. What is this volume of water in litres is required to fill the fish tank?
Think: Think about the steps needed to move from cm^{3} to litres. (cm^{3}$\rightarrow$→mL$\rightarrow$→L). We know that $1$1 cm^{3} 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$350000 cm^{3}$=$=$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 (cm^{3}) to litres (L).
A small pond contains $3900$3900 L of water. What is the volume of the pond (in m^{3})?
use metric units of volume, their abbreviations, conversions between them, and appropriate choices of units
understand the relationship between volume and capacity
estimate volume and capacity of various objects