Estimating volume and capacity

In a nutshell

The volume of a shape tells you how much space it takes up. You can measure the volume by counting squares or using a formula. Liquids also take up volume. Objects such as containers and jugs have a capacity.

Volume

Volume is the measurement of how much space a 3D shape takes up. It can be measured in different units such $mm^3, cm^3$ and $m^3$ .

Using cubes to find the volume

Cubes with a given length can be used to work out volume.

Example 1

Find the volume of the cuboid, by counting the cubes.

$1 \ cube =1cm^3$

Firstly, count the number of cubes in the cuboid.

The cuboid is made up of $12$ cubes.

Since each cube is $1cm^3$ multiply this by $12$ to find the total volume.

The volume of the cuboid is $\underline{12cm^3}$ .

Using the formula to find the volume

The volume of a cuboid can be found using the following formula:

V=l \times w \times h

$V$	The Volume of the cuboid.
$l$	The length of the cuboid.
$w$	The width of the cuboid.
$h$	The height of the cuboid.

Example 2

Find the volume of the cuboid using the formula.

Maths; Measurement; KS2 Year 5; Estimating volume and capacity

$height = 3cm, \ width = 2cm, \ length = 5cm$

Substitute the values for height, width and length in to the formula.

$\begin{aligned}Volume &= l \times w \times h \\Volume &= 5 \times 2 \times 3 \\Volume &= \underline{30cm^3}\end{aligned}$

Capacity

Liquids also have a volume which takes up space in a given vessel, such as a jug. The jug's capacity is the maximum volume of liquid it may hold.

Example 3

Determine the capacity of the jug.

Maths; Measurement; KS2 Year 5; Estimating volume and capacity

The jug is filled up to $1300ml$ . However, the maximum capacity of the jug is $1500ml$ .

The capacity of the jug is $\underline{1500ml}$ .