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4.06 Units of volume and capacity

Lesson

Volume vs capacity

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 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.

 

Units of volume

Common units for volume from smallest to largest are:

  • millimetres cubed (mm3)
  • centimetres cubed (cm3)
  • metres cubed (m3)

 

Units of capacity

Common units for capacity from smallest to largest are:

  • millilitres (mL)
  • litres (L)
  • kilolitres (kL)
  • megalitres (ML)

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.

 

Estimating volume and capacity

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:

  • $1$1 mm3 is very small! This is a cube with length, width and height $1$1 mm - about the size of $30$30 grains of salt.
  • $1$1 cm3 is the size of a cube with length, width and height $1$1 cm - this is about two m&ms. A teaspoon holds $5$5 cm3.
  • $1$1 m3 is the size of a cube with length, width and height $1$1 m - about the size of a fridge.
  • $1$1 mL is the same as $1$1 cm3 and a teaspoon is $5$5 mL.
  • $1$1 L. It is very common for milk to come in $1$1 and $2$2 litre cartons.
  • $1$1 kL is one thousand litres. This is equal to $1$1 m3, and is around $6$6 bathtubs full of water.
  • $1$1 ML is one million litres - this is a lot of liquid! An Olympic swimming pool holds on average $2.5$2.5 ML.

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.

 

Practice questions

Question 1

When referring to the capacity of a pool, which of the following could be an appropriate unit to use? Select all correct options.

  1. mL

    A

    L

    B

    ML

    C

    mL

    A

    L

    B

    ML

    C

Question 2

Which of the following objects' volumes are usually measured in cubic centimetres?

Select all that apply.

  1. The volume of air in a hall

    A

    The volume of an empty bottle

    B

    The area of a sheet of paper

    C

    The amount of air in a balloon

    D

    The volume of air in a hall

    A

    The volume of an empty bottle

    B

    The area of a sheet of paper

    C

    The amount of air in a balloon

    D

Question 3

What is the best estimate for the volume of liquid in this container if it is able to hold $3600$3600 millilitres when full?

  1. $2200$2200 millilitres

    A

    $1800$1800 millilitres

    B

    $1200$1200 millilitres

    C

    $3200$3200 millilitres

    D

    $2200$2200 millilitres

    A

    $1800$1800 millilitres

    B

    $1200$1200 millilitres

    C

    $3200$3200 millilitres

    D

 

Converting units of volume

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.

Remember!

When converting between units of volume:

  • Multiply if converting to a smaller unit - more smaller cubes will be needed to fill the same space
  • Divide if converting to a larger unit - less larger cubes will be needed to fill the same space
  • Multiply or divide by the conversion factor for lengths three times (or cubed)

 

Worked example

Example 1

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 m3 to cm3 is $1000000$1000000, which can be remembered as multiplying by conversion from metres to centimetres three times.

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

 

Converting units of capacity

The following diagram shows the conversion factor between common units for capacity:

Note: The conversion factor is $1000$1000 at each step.

 

Converting between units

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.

 

Worked example

example 2

A fish tank is $350000$350000 cm3. What is this 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

 

Practice questions

Question 4

Convert $4920$4920 millilitres to litres.

  1. $4920$4920 millilitres = $\editable{}$ litres.

Question 5

Convert $6750$6750 cubic centimetres (cm3) to litres (L).

Question 6

A small pond contains $3900$3900 L of water. What is the capacity of the pond (in m3)?

Outcomes

ACMEM027

use metric units of volume, their abbreviations, conversions between them, and appropriate choices of units

ACMEM028

understand the relationship between volume and capacity

ACMEM029

estimate volume and capacity of various objects

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