Lesson video

Hi, I'm Miss Davies, and in this lesson we're going to be finding the volume of cuboids and cubes.

Let's look at this first example.

We've got a cuboid that is four centimetres by three centimetres by five centimetres.

We've also got this little blue cube, which is one centimetre by one centimetre by one centimetre.

The volume of this little cube is one centimetre cubed.

Volume is always measured in cubic units.

For example, centimetres cubed, millimetres cubed, kilometres cubed, or metres cubed.

How many little cubes can we fit inside of this cuboid? This will give us the volume of the cuboid.

We can fit four cubes across the cuboid like this, because the width of the cuboid is four centimetres.

We can fit three of these rows like this, because the height of the cuboid is three centimetres.

All together, we have got four times three cubes, or 12 cubes.

Let's call this a layer.

How many layers of the cubes can we fit inside this cuboid? We can fit five layers of these cubes into our cuboid, because the length of the cuboid is five centimetres.

This means that we have got 60 little cubes, or 60 centimetres cubed.

This is the volume of the cuboid.

We can generalise this as the volume of a cuboid is equal to the width multiplied by the height multiplied by the length.

Let's have a look at another example.

We've just found out that the volume of a cuboid can be worked out by multiplying together the width and the height and the length.

The width of this rectangle is 4.

2 metres.

The height is eight metres, and the length is 1.

5 metres.

If we multiply these three numbers together, we get 50.

4 metres cubed.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

To find the volume of a cuboid, you multiply together the width, the height, and the length.

Don't forget that the units are cubed.

This is a special kind of cuboid.

The name given to it is a cube.

All of the lengths of a cube are the same.

We know, to work out the volume of a cuboid, we multiply the width by the height by the length.

In this example, these are all six.

The volume of this cube is 216 centimetres cubed.

We can generalise this as a multiplied by a multiplied by a, or a cubed.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Because all of the lengths of a cube are equal, multiplying the width, height, and length together is the same as doing the length cubed.

The volume of this cuboid is 126 centimetres cubed.

We've been asked to work out the value of the length p.

We know that the volume of a cuboid is found by multiplying together the width, the height, and the length.

We can substitute in the values that we know.

126 is equal to six times seven times p.

We can rewrite this as 126 equals 42 times p.

Using inverse operations, we know that p is equal to 126 divided by 42.

This means that p is equal to three centimetres.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Multiply together the given lengths and then divide the volume by this value.

What is different about this example compared to questions that we've looked at before? Well done if you noticed that two of the lengths are in metres and one of the lengths is in centimetres.

In order to work out the volume, we need to make sure that all of the lengths are in the same units.

Let's convert 420 centimetres into metres.

This is 4.

2 metres.

We know, to work out the volume of a cube, we multiply the width by the height by the length.

If we substitute our values into this, we have 4.

2 multiplied by six multiplied by 8.

5.

This gives us an answer of 214.

2 metres cubed.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Make sure that all of the lengths are measured in the same units before multiplying them together to get the volume.

This diagram shows the net of a cuboid.

The net is a diagram that shows the flattened version of a three D shape.

If we form the cuboid using this net, it would look like this.

We can then work out the volume of the cuboid.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

Think about the cuboid that this net would form.

We need to multiply together 20, 12, and eight to give the answer of 1,920 centimetres cubed.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

There are two ways to work out this problem.

The first is to calculate the volume of both the container and the box in the same units.

This would be 21 metres cubed and 0.

2 metres cubed.

We can then do 21 divided by 0.

2 to give 168 boxes.

The second way is to work out how many boxes would fit along each length.

This would be four, 14, and three.

You can then multiply these numbers together to give 168 boxes.

That's all for this lesson.

Thanks for watching.