Lesson video

Welcome to lesson seven in our decimals and measures topic.

Today we'll be learning to calculate the volume of cubes and cuboids.

Just a pencil and piece of paper needed for the lesson, so pause the video and get your equipment now.

Here's our agenda for today.

So we'll be looking at the volume of cubes and cuboids, starting with a quiz to test your knowledge from our previous lesson.

Then we'll look at what volume is, a formula for calculating volume before we look at some volume problems and then you'll do some independent learning and a final quiz.

So let's start with out initial knowledge quiz.

Pause the video now and complete the quiz and then restart once you've finished.

Good job, so let's begin with what volume is.

Volume is the amount of space a 3D shape takes up.

So here we have a picture of a cube, which has a height of one centimetres, a width of one centimetre and a depth of one centimetre.

Therefore, it has a volume of one centimetre cubed.

So here we have a cuboid and we have the dimensions of the cuboid.

I want you to have a think about using your knowledge of the cube, what could the volume of the cuboid be? So the cuboid is made up of two centimetre cubes.

A one-centimeter has a volume of one cubic centimetre.

So two cubes has a volume of two cubic centimetres.

And you can see that the volume of the second cuboid is double that of the first cube.

So this has a volume of two centimetres cubed.

Let's look at some more shapes.

A cube has been built, which is twice as high, twice as deep and twice as wide as the cuboid.

So what are its new dimensions and what will its volume be? Pause the video while you do this problem.

So this cube is made up of eight one-centimeter cubes.

Therefore, it has a volume of eight cubic centimetres.

Its dimensions are two centimetres high, two centimetres wide and two centimetres deep.

So can you see a connection between the dimensions and the volume? Let's think about this on our next slide.

So Yasser has noticed something about the cuboid.

He says that the first one has a volume of one centimetre cubed.

And he's noticed that if he multiplies the height by the depth, by the width, the answer is one centimetre cubed.

So he did one times one times one, which gave him one centimetre cubed.

And then he's noticed that this is the same for other cuboids.

So if we look at this one.

It's one by two by one.

One times two times one is two centimetres cubed.

And it's made up of two of those centimetre cubes.

Let's look at this third one together.

The dimensions are two by two by two.

Two times two times two is eight centimetres cubed.

And we know that this is made up of eight of those one-centimeter cubes.

So I wonder now if you can think of a formula for finding the volume of a cube or a cuboid.

Pause the video and write down your formula.

So we can infer then that length times width times depth is equal to volume.

So this is the formula that we're going to use in today's lesson to calculate the volume of 3D cubes and cuboids.

We'll start off with a cereal packet.

It has dimensions of eight centimetres deep, 20 centimetres wide and 35 centimetres high.

So we're going to calculate the volume of the box.

Remember, this is our formula.

So we're doing length times width times depth.

So we're doing 20 times eight times 35.

And remember that we know that multiplication is commutative, so we can do these in any order.

I haven't actually started with the length here or put the depth at the end.

They can be put in any order.

And the reason why it's important that we rearrange them is that we use our known facts to support our multiplication.

So I've actually put 20 first because I know that if I know two times eight is 16, then I know that 20 times eight is 160.

So I've used my known facts to do the first part of the question.

Then the second part, I'll be using long multiplication.

160 multiplied by 35, gives us a volume of 5,600 centimetres cubed.

Now it's your turn.

Pause the video and calculate the volume of the book.

So you will have worked out that we were looking here at 18 times three times 23 and the total volume is 1,242 centimetres cubed.

Now we're going to apply our knowledge of calculating volume to some word problems where we specifically have missing lengths.

So here's our first problem.

Zak is creating a vivarium for his pet baby tortoise, Voldetort.

So a vivarium is a little home or a tank to house a tortoise.

He knows that the volume of the vivarium has to be 200 metres cubed and that the base needs to be large enough for Voldetort to move around and explore.

And we need to think about what could the dimensions of the vivarium be? So what we're looking for here is three numbers that multiply to give the product of 200.

And we can use the factors of 200 to help us out with this.

So I've used a factor bug and I've given some of the factors of 200.

I haven't given all of them.

So I want you to have a think about this now.

How much these factors help me to calculate the dimensions of the cuboid? So what I've done here is I've taken it a little bit further.

Because I need to find three numbers that multiply together to give me 200, I've had to split the numbers down further into further factors.

So I know, I'll start with the first one, I know that eight times 25 is equal to 200 and if I multiply that by one, I still get 200.

So I could make a vivarium that is one metre deep, eight metres wide and 25 metres tall.

That's going to take up an awful lot of space in the room.

So this might not be the most practical dimensions.

Let's have a look at another one.

I know that two times 100 is equal to 200 but I need three numbers that multiply together.

So I can look at the factors of 100 and I know that 100 is the product of 10 times 10.

Therefore, I could do two times 10 times 10, which will give me 200.

And I'll show you one more example.

In this one, I've worked out that I could use the dimensions five times eight times five.

And I know that five multiplied by 40 gives me 200 but if I look at the factors of 40, I knew that eight times five is 40.

Therefore, rather than doing five times 40, I can do five times eight times five and you're going to have another question like this in your independent task.

So you need to think about drawing out a factor bug but then going further and thinking about other factors of these numbers so that you can multiply three numbers together to find the volume.

That's all the input that you're going to get from me.

I want you to pause the video now so that you complete some independent learning and then click Restart once you're finished and we'll go through the questions together.

So for question one, you had three cuboids and you were asked to calculate the volume of each.

Remember, length times width times depth gives us volume.

So for your first one, you're multiplying four by four by 10.

5.

So you may have done four times four first in your head and then done the rest as long multiplication.

And that gives you 168 centimetres cubed.

You must remember that part of your units because that tells us that it's the volume of the shape.

For your next one, your answer's going to be in metres cubed.

One times 0.

9 times 6.

5 gives you 5.

85 metres cubed.

And your last one is in millimetres cubed.

40 times 50 times 38, so you probably did four times five and then multiplied that by 100 and multiplied that by 38 to give you 76,000 millimetres cubed.

Onto another dimension problem.

This time Dan is looking to build an aquarium with a volume of 600 metres cubed.

So I recommended that you drew out a factor bug.

And then you could work on sketching four possible cuboids.

So the first one I started with was two times 300 and multiply that by one.

So you could do that for all of them.

You could just do three times 200 multiplied by one.

But let's make it more interesting.

I've added in some different ones.

So here I did, I knew that 300 is three times 100 and multiplied that by two.

And then I looked at 150.

I knew that 150, two factors of three and 50.

So I could do four times three times 50 and so on.

And you will have come up with different examples to me.

So you're looking at any of these numbers on the right and thinking about factors of those that could then be multiplied by the numbers on the left.

For question three, a toymaker has made wooden buildings and we have to figure out the dimensions of them first, given only the width of the bottom being 24 centimetres, the depth of five centimetres and the height of the smaller building of seven centimetres.

So we were given this information.

The tall building is twice the height of the short building.

So now you know that the tall building is twice the height of seven centimetres.

So it's 14 centimetres.

The short building, that's this one, is twice as wide as the tall building.

So what you needed to do here was to look at the total width of 24 centimetres, divide it into three parts because we know that this takes up one of the parts and then the shorter building, two of the parts, so it's twice the width of the smaller one.

So then the taller building has a width of eight centimetres and the shorter building has a width of 16 centimetres.

So now we've got our dimensions, we can calculate the volume.

So the taller building is 14 centimetres high, eight centimetres wide and it has a depth of five centimetres.

14 times eight times five is 560 centimetres cubed.

So that's the volume of the first building.

The second building is seven centimetres high, five centimetres deep and 16 centimetres wide, which also gives us a volume of 560 centimetres cubed.

And we were asked for the total volume.

So those two numbers needed to be added together to give the total volume of 1,120 centimetres cubed.

Onto your last question.

You were asked to find the missing length for cuboid B since these two shapes have the same volume.

So the first job is to calculate what is the volume of the shapes? So shape A, we know that that's a cube.

So we're multiplying eight by eight by eight, which gives us a volume of 512 centimetres cubed.

So we know now that B has that volume.

So we know that eight times four times c is equal to 512 centimetres cubed.

And we can do a bit more to that, so we know that 32 multiplied by c, gives us 512 centimetres cubed.

So we have to use our knowledge of the inverse here.

512 divided by 32 is equal to c.

Therefore c is equal to 16 centimetres.

And it's always wise to go back and check, using the inverse.

So eight times four times 16, that gives us 512 centimetres cubed.

Now it's time for your final quiz.

So pause the video and complete the quiz and click Restart once you're finished.

You did a great job in today's lesson.

In our next lesson, we'll be converting between standard units of mass.

I'll see you then.