Conversions from volume to capacity is the mathematical equivalent of asking
"How much water can we pour into this container?"
What is capacity?
Capacity is a measure of how much a container can hold. We normally associate capacity with liquids, but it can also be used as a measure of gasses and solids.
When measuring the capacity of containers for everyday use, we will often use either millilitres (mL) or litres (L). For larger containers like bathtubs or swimming pools, we can use kilolitres (kL).
We can convert between these units using the conversion equations:
- $1$1 L$=$=$1000$1000 mL
- $1$1 kL$=$=$1000$1000 L
Worked Examples
Example 1
Convert $14500$14500 mL to L.
Think: To convert from millilitres to litres, we want to find how many litres there are in $14500$14500 millilitres. Since $1$1 L$=$=$1000$1000 mL, we can find how many litres there by finding how many sets of $1000$1000 fit into$14500$14500.
Do: We can find how many sets of $1000$1000 fit into $14500$14500 using division.
| $14500$14500 mL | $=$= | $\frac{14500}{1000}$145001000 L |
Divide by the conversion factor |
| $14500$14500 mL | $=$= | $14.5$14.5 L |
Perform the division |
Example 2
Convert $3.24$3.24 kL to L.
Think: To convert from kilolitres to litres, we want to find how many litres there are in $3.24$3.24 kilolitres. Since $1$1 kL$=$=$1000$1000 L, we know that the number of litres will be $1000$1000 times more than the number of kilolitres.
Do: We can find how many litres there are by multiplying the number of kilolitres by $1000$1000.
| $3.24$3.24 kL | $=$= | $3.24\times1000$3.24×1000 L |
Multiply by the conversion factor |
| $3.24$3.24 kL | $=$= | $3240$3240 L |
Perform the multiplication |
Reflect: When converting from a smaller unit to a larger unit (as seen in the first example) we divide by the conversion factor. When converting from a larger unit to a smaller unit (as seen in the second example) we multiply by the conversion factor.
Practice question
Question 1
Convert $99000$99000 L to kL.
Converting from volume to capacity
When converting from volume to capacity, there is only one conversion equation that we need to use:
$1$1 cm3$=$=$1$1 mL
This tells us that every one cubic centimetre has a capacity of one millilitre. It also tells us that any conversion equations involving millilitres will work the same way for cubic centimetres.
This means we get this conversion equation for free:
$1000$1000 cm3$=$=$1$1 L
Now we have a way to convert from volume to capacity, we can start finding the capacity of containers.
The capacity of a cubic metre
As mentioned before, the only conversion we need in order to convert between volume and capacity is the equality $1$1 cm3$=$=$1$1 mL.
With this in mind, how many litres are there in one cubic metre?
To find how many litres there are in one cubic metres, there are two conversions we need to make. First, we want to convert our cubic metre into cubic centimetres. Once we have done this, we can then convert to litres, like so:
| Volume | $=$= | $1$1 m3 | |
| Volume | $=$= | $1$1 m$\times$×$1$1 m$\times$×$1$1 m |
One cubic metre is a cube of side length $1$1 m |
| Volume | $=$= | $100$100 cm$\times$×$100$100 cm$\times$×$100$100 cm |
Convert each dimension from metres to centimetres |
| Volume | $=$= | $100\times100\times100$100×100×100 cm3 |
Combine the units to get cubic centimetres |
| Volume | $=$= | $1000000$1000000 cm3 |
Perform the multiplication |
These calculations tell us that one cubic metre is equal to $1000000$1000000 cubic centimetres. Now that our volume is in cubic centimetres, we can convert to capacity. We can convert using the equation $1$1 L$=$=$1000$1000 cm3:
| Capacity | $=$= | $\frac{1000000}{1000}$10000001000 L |
Divide by the conversion factor |
| Capacity | $=$= | $1000$1000 L |
Perform the division |
So the capacity of one cubic metre is $1000$1000 litres.
To convert from capacity back into volume, we can simply reverse these steps.
Worked Example
A fish tank has a capacity of $6.58$6.58 kL. What is its volume in cubic metres?
Think: To find the number of cubic metres, we want to convert the capacity into litres and then convert from litres into cubic metres.
Do: When converting from kilolitres to litres the unit is getting smaller so we multiply by the conversion factor.
| $6.58$6.58 kL | $=$= | $6.58\times1000$6.58×1000 L |
Multiply by the conversion factor |
| $6.58$6.58 kL | $=$= | $6580$6580 L |
Perform the multiplication |
We can then convert from litres to cubic metres, remembering that one cubic metre equates to $1000$1000 litres. We can find how many cubic metres are filled by $6580$6580 litres by dividing by $1000$1000.
| $6580$6580 L | $=$= | $\frac{6580}{1000}$65801000 m3 |
Division by $1000$1000 |
| $6580$6580 L | $=$= | $6.58$6.58 m3 |
Perform the division |
As such, the volume of the fish tank is $6.58$6.58 m3.
Reflect: Notice that the volume in cubic metres is equal to the capacity in kilolitres. This tells that one cubic metre equates to one kilolitre.
Volume and capacity are not the same thing. An object will always take up space (volume), but it may not have capacity. A solid, for example, has volume but no capacity. The capacity of an object will also depend on its design; it may not be the same as the volume. For example, a vase may have a solid chunk of glass for its base resulting in less capacity than volume.
In real-life experiences, units of volume and capacity may be used interchangeably.
Practice question
Question 2
Kathleen is constructing a swimming pool designed to hold $34.4$34.4 kilolitres of water.
She has already decided on a base area of $8$8 square metres.
What will the volume of Kathleen's pool be?
Give your answer in cubic metres.
If the depth of the pool is the same at every point, how deep must it be?
Give your answer in metres.