Look at this cube. It has a length, a width and a height of $1 cm$.
It is called a centimetre cube. You say that it has a volume of one cubic centimetre (1 cm3).

This cuboid $4 cm$ long, $3 cm$ wide and $2 cm$ high.
If you divide the cuboid into centimetre cubes, it looks like this.

You can see that there are 12 cubes in each layer and that there are two layers. This means that the total number of centimetre cubes in this cuboid is 24.
You say that the volume of the cuboid is $12c{m^3}$.
You can work out the volume of a cuboid, using the formula:
volume = length $ \times $ width $ \times $ height
or $V = l \times w \times h$

If the sides of a cuboid are measured in millimetres, the volume will be in cubic millimetres (${mm^3}$).
If the sides of a cuboid are measured in metres, the volume will be in cubic metres (${m^3}$).

a: Work out the volume of this cuboid.
b: A concrete cuboid has a length of $5/1 m$, a width of $3/2 m$ and a height of $1/8 m$.
i- Work out the volume of the cuboid.
ii- Use estimation to check your answer.

a: $V = 8 \times 5 \times 3$
Use the formula: volume = length $ \times $ width $ \times $ height.
$ = 102c{m^3}$
All the lengths are in cm so the answer is in cm3.
b: $V = 5/1 \times 3/2 \times 1/8$
Use the formula: volume = length $ \times $ width $ \times $ height.
$ = 29/376{m^3}$
All the lengths are in m so the answer is in ${m^3}$.
ii- $V = 5 \times 3 \times 2$
To estimate, round all the lengths to the nearest whole number.
$ = 30{m^3}$
30 is close to 29/376 so the answer to part bi is probably correct.

1) Work out the volume of each of these cuboids.

2) Work out the volume of each of these cuboids.

Make sure you write the correct units with your answers.

3) This is part of Steph's homework.

A cuboid hasa lengthof $12 cm$, a width of $9 cm$ and a height of $35 mm$.
What is the volume of the cuboid?

Volume $ = 12 \times 9 \times 35$
$ = 3780c{m^3}$

Steph has got the solution wrong.
Explain the mistake that Steph has made and work out the correct answer for her.

4) The table shows the length, width and height of four cuboids.

Volume	Height	Width	Length
$......m{m^3}$	$6mm$	$12mm$	$5cm$	a
$......c{m^3}$	$4mm$	$8cm$	$12cm$	b
$......{m^3}$	$90cm$	$6cm$	$8m$	c
$......c{m^3}$	$25cm$	$60cm$	$1/2m$	d

Copy and complete the table.

5) A metal cuboid has a length of $3/2 m$, a width of $4/8 m$ and a height of $2/1 m$.
a: Work out the volume of the cuboid.
b: Check your answer using estimation.

6) Alicia buys a fish tank.
The dimensions of the fish tank are shown in the diagram.
Alicia fills the tank with water to $\frac{4}{5}$ of the height of the tank.
What is the mass of the water in the fish tank?