You may also like

problem icon

Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

problem icon

Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

problem icon

Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

The Big Cheese

Stage: 2 Challenge Level: Challenge Level:1

I met up with some friends yesterday for lunch. On the table was a good big block of cheese. It looked rather like a cube. As the meal went on we started cutting off slices, but these got smaller and smaller! It got me thinking ...

What if the cheese cube was $5$ by $5$ by $5$ and each slice was always $1$ thick?

It wouldn't be fair on everyone else's lunch if I cut up the real cheese so I made a model out of multilink cubes:

You could of course, just make $5$ slices but I wanted to have a go at something else - keeping what is left as close to being a cube as possible.

You can see that it's a $5$ by $5$ by $5$ because of the individual cubes, so the slices will have to be $1$ cube thick.

So let's take a slice off the right hand side, I've coloured it in so you can see which bit I'm talking about:

  This now gets cut off and we have:   
 

The next slice will be from the left hand side (shown in a different colour again):

Well the knife cuts and we are left with: 
 

Remember I'm setting myself the task of cutting so that I am left with a shape as close to a cube shape as possible each time.

So the next cut is from the top. Hard to cut this so I would have put it on its side!

I'll remove that and I'm left with the $4$ by $4$ by $4$ cube


I do three more cuts to get to the $3$ by $3$ by $3$ and these leave the block like this:

 
I'm sure you've got the idea now so I don't need to talk as much about what I did:
  and then onto:

That leaves you with two of the smallest size cube $1$ by $1$ by $1$.

If we keep all the slices and the last little cube, we will have pieces that look like (seen from above):

C H A L L E N G E

Now we have thirteen objects to explore.
  • What about the areas of these as seen from above?
  • What about the total surface areas of these?
  • What about their volumes of the pieces?

A L S O

Investigate sharing these thirteen pieces out so that everyone gets an equal share.


What about ...?

I guess that once you've explored the pattern of numbers you'll be able to extend it as if you had started with a $10$ by $10$ by $10$ cube of cheese.