Calculating volume

Volume is the amount of space occupied by a solid, liquid or a shape.

Let’s find the volume of a shape. The formula for calculating the volume of a cuboid is:

Volume = length × width × height

Or you could write this as:

V = l × w × h

It is important to know how much space objects take up.

For example, in a warehouse, they need to know the volume of the boxes, so they know how much stock they can fit in.

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When you are thinking about the volume of a shape, you always use a cubic measurement.

A 1cm cube takes up 1cm³ of space.

When you calculate the volume you are thinking about how many of these 1cm³ cubes will fit in the space.

You represent this cubic measurement by writing a small ‘3’ at the end of the measurement. For example ____ cm³.

The volume of a shape can be measured in mm³, cm³, m³, and km³.

The unit of measure you use depends on the size of the shape.

Calculating the volume of a cuboid

To calculate the volume of a cuboid you multiply the three dimensions together.

The three dimensions are:

The formula for calculating the volume of a cuboid is:

Volume = length × width × height

V= l × w × h

Now, let’s find the volume of this cuboid. It is not drawn to scale.

You can use the formula:

V= l × w × h

First replace the letters with the measurements.

V = 6cm × 2cm × 5cm

Now multiply these values together.

V = 60cm³

Remember, you can multiply the dimensions in any order because multiplication is commutative.

Finding the volume of a compound shape

A compound shape is a shape made up of other recognisable shapes.

This is a compound shape. It is made up of a cube and cuboid.

You find the volume of a compound shape in the same way.

V= l × w × h

You find the volume of each shape and then add them together to find the total volume.

First let’s work out the volume of the cube.

V = 2cm × 2cm × 2cm

V = 8cm³

Now let’s work out the volume of the cuboid.

V = 2cm × 2cm × 6cm

V= 24cm³

Next you add these together to find the total volume.

8cm³ + 24cm³ = 32cm³

V = 32cm³

So the total volume of this compound shape is 32cm³.

A cube is different to other cuboids because all its dimensions are equal in length. However, you can still use the same formula to calculate the volume.

Example 2

To find the volume of a cuboid you need to multiply all the dimensions together.

Example 3