Capacity of a container practice questions | Year 9 Mathematics (Measurement, Volume and capacity)

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 \(\displaystyle V=0.084\text{ m}^3\;\to\;C=84\text{ L}\)

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 large

Using 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 cubed

Including 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 volume

Difficulty levels

introConvert a stated volume in cubic centimetres directly to litres

standardCalculate a rectangular container's volume, then convert it to mL or L

challengeUse base area and depth to judge whether a container has enough capacity, or convert a triangular-prism volume to capacity

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 I use a calculator?+

A calculator is allowed unless a question is marked no calculator

Which year level and chapter is this?+

Year 9 Mathematics, chapter 5: Measurement

In this chapter