KS3 Maths: Volume

Pump up the volume,Pump up the volume,Pump up the volume,Check it out…

WHO NEEDS VOLUME?

Sorry, you need volume. Volume is the measure of the space taken up by three-dimensional objects. And pretty much all of your possessions are three-dimensional objects. Your hat, your cat, your bat. It doesn't even have to rhyme with hat. Everything you own takes up space. How much space? VOLUME?

I mean, look, I've got no space left in this room. It's just full of junk I don't even use any more. Look. Legs! I've got a perfectly good pair in my trousers. What have I got? Yes! This, 100 copies of this. The Sanjeev workout plan. Why didn't that sell? Space hopper. I take the bus now. What else? Ukulele… Why didn't that career take off? The old ball pit. I mean, phff, the number of nights I've spent in that. But I need to get rid of it all. I need to free up some space. I need to put all this stuff up in storage and frankly it's too big a job for one man. I think I'm going to need some help.

And this is why I keep this man, Gavin, in my cupboard. Gavin, you are, are you not, an expert in volume?

I am.

How so?

I run a removals and storage company and for every job we do, we need to have an accurate volume of the job so we know what's going to fit in boxes, or what's going to fit in our vans and containers.

So, can I ask you, using that volume brain, to hazard a guess as to the total volume of the stuff I need to take out of here and put in storage?

Total volume…including the furniture is five million cubic centimetres or five cubic metres.

Now that's a lot of cubic centimetres but will it all fit in Gavin's wee van?

Now let's start with the ball pit, yeah? Erm, I'm actually quite sad to see this go. I've got quite attached to this. I even gave all the balls a name, so that one's called Derek. OK, right, can you help me work out the volume of this ball pit, please?

Sure.

What have you got?

80 centimetres.

And I also have 80 centimetres. Er, but it is a cuboid so we need to measure the height as well, don't we?

We do indeed. And the height's 30 centimetres.

OK so that's 80 x 80 x 30. So it's 192,000 cubic centimetres. Is there room in your van for this?

Plenty!

OK, let's take it, come on!

Gavin's van only holds five cubic metres. Let's hope his estimate of my stuff is right. Or it could be two trips!

Gavin, check me out! I've found some old clothes.

Nice! But maybe we should stop monkeying around and get this stuff packed.

Fair enough, have you got something we could put this in?

Yeah, we could put it in here. Do you remember how to calculate the volume of a cylinder?

Yes, I do. Er, we need some measurements, don't we? We need to measure the height of the cylinder first of all.

The height is 48 centimetres.

OK and then we need the radius so if you can do the diameter.

The diameter is 46 centimetres.

Which means the radius is half the diameter, which is 23 centimetres so now I've got an equation. So that's 79,730.88 cubic centimetres of my old clothes. In you go!

The success of Gavin's business relies on accurate volume calculations. The wrong measurement of even the smallest objects can make or break a job.

Right, I think that's everything packed. I think we've done it.

Everything except for the sticky notes!

Oh, disaster! Have we not accounted for these? Can we get these in your van? Better measure them. That's er, 7.6 centimetres…by 7.6 centimetres by… by 7.6 centimetres!

Yeah, I think we can squeeze it in.

Oh, thank Harry Styles! Right, come on. Let's get this stuff into the van. Come on!

Great. Gavin was right. It did all fit into his wee van. Happy days! But even happier days because get this… I don't have to move it any more because I found a brilliant empty room to store it all in! How did I miss it? Honestly, I'm so unobservant sometimes. There's only one question remains. Does it have enough volume?