Volume and capacity
Find the usable volume from the internal dimensions first. Then convert the cubic volume to the requested capacity unit
\[\begin{gathered}V=lwh\\1\text{ L}=1{,}000\text{ cm}^3\\1\text{ m}^3=1{,}000\text{ L}\end{gathered}\]
- Use the usable dimensions Multiply the internal length, width and height for a rectangular container \(\displaystyle \begin{gathered}V=40\times25\times30\\=30{,}000\text{ cm}^3\end{gathered}\)
- Keep cubic units together The result of multiplying three lengths is a volume in cubic units \(\displaystyle \text{cm}\times\text{cm}\times\text{cm}=\text{cm}^3\)
- Convert cubic centimetres Divide by 1000 for litres, while one cubic centimetre is one millilitre \(\displaystyle \begin{gathered}30{,}000\text{ cm}^3\div1{,}000\\=30\text{ L}=30{,}000\text{ mL}\end{gathered}\)
- State capacity in mL or L Capacity describes how much the container can hold, using a liquid-capacity unit \(\displaystyle V=0.084\text{ m}^3\;\to\;C=84\text{ L}\)
- Cylindrical containers Use internal radius r and the actual usable or filled depth h, both measured in centimetres. The capacity C is in litres. Keep π exact until the final answer \(\displaystyle C=\pi r^2h\div1{,}000\)
Worked example
A rectangular storage container has internal length 70 cm, width 40 cm and height 30 cm. Find its volume and capacity in litres
\[\begin{gathered}l=70\text{ cm},\quad w=40\text{ cm}\\h=30\text{ cm}\end{gathered}\]
- \(\displaystyle \begin{gathered}V=lwh=70\times40\times30\\=84{,}000\text{ cm}^3\end{gathered}\)Multiply the three internal dimensions to find the usable volume
- \(\displaystyle 1\text{ L}=1{,}000\text{ cm}^3\)Use the cubic-centimetre to litre conversion
- \(\displaystyle C=84{,}000\div1{,}000=84\text{ L}\)Dividing the volume by 1000 gives the container's capacity
Common mistakes
Using the wrong cubic conversion factor
✕\(\displaystyle 56{,}000\text{ cm}^3\div100=560\text{ L}\)✓\(\displaystyle 56{,}000\text{ cm}^3\div1{,}000=56\text{ L}\)
One litre is 1000 cm³, so dividing by 100 produces a capacity ten times too largeUsing a length factor for a volume
✕\(\displaystyle 84{,}000\text{ cm}^3\div100=840\text{ m}^3\)✓\(\displaystyle \begin{gathered}84{,}000\text{ cm}^3\div100^3\\=0.084\text{ m}^3\end{gathered}\)
Each of the three length dimensions changes, so the conversion factor must be cubedIncluding an outside measurement
✕\(\displaystyle \begin{gathered}V=70\times40\times30\times4\\=336{,}000\text{ cm}^3\end{gathered}\)✓\(\displaystyle \begin{gathered}V=70\times40\times30\\=84{,}000\text{ cm}^3\end{gathered}\)
The stated dimensions are already internal usable dimensions, so an outside thickness is not multiplied into the volumeDifficulty levels
introConvert a stated volume in cubic centimetres directly to litres
standardCalculate a rectangular container's volume, then convert it to mL or L
challengeJudge capacity against a requirement or find triangular-prism and cylindrical capacities
examChoose the capacity from values containing incorrect capacity and volume-conversion factors
Questions about this topic
Why is 1000 used when converting cm³ to L?+
One litre has the same volume as 1000 cubic centimetres, so a volume in cm³ is divided by 1000 to obtain litres
What is the difference between volume and capacity?+
Volume is the amount of three-dimensional space occupied by an object or a region. A container’s capacity is its usable internal volume, often expressed in mL or L
How are millilitres related to cubic centimetres?+
One millilitre is exactly equal to one cubic centimetre, so the numerical value stays the same when changing between mL and cm³
Can an open-top tank still have a cylindrical capacity?+
Yes. Capacity measures internal space up to the usable height; it does not count faces or require a lid
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 1: Measurement
In this chapter
Convert measurement unitsPerimeter of standard shapesFind an unknown side from a perimeterCircumference of a circlePerimeter of composite shapesArea of standard shapesArea of a circleArea of a sectorArea of composite shapes1F Prism surface area: Surface area of solidsSurface area of a triangular prismExposed surface area of joined cuboids1G Cylinder surface area: Surface area of solidsSurface area of a cylinder portionSurface area of a cylinder joined to a cuboidVolume of prisms and cylindersCapacity of a containerVolume of a cylinder portionJoined and hollow prism-cylinder volumesModel rainwater collection and storageSmallest unit and limits of accuracyMeasurement bounds in calculationsVolume of cones, pyramids and spheres (optional extension)1J Level 10A extension: pyramids, cones and spheres: Surface area of solids (optional extension)Surface areas of advanced solids and composites (optional extension)