Maths Week Scotland 2022 - Problem 1 - Counting Cubes

CHRIS: This problem is all about visualising 3D shapes and counting cubes.

The diagram shows a large cube that has cross shaped holes punched through each face.

How many individual cubes would be needed to construct it?

So I want you to imagine, if you can, a cube which is five by five by five.

Right so a big cube made up of smaller cubes: five cubes by five cubes by five cubes.

PUPILS:

Try building the up yourself using some building blocks.

It might help to think about the whole cube in sections or in layers.

Another way would be to look at the cross shapes and figure out how many blocks have been removed.

Good luck!

This challenge was all about visualising 3D shapes and counting cubes.

Let’s start by looking at the large cube.

One way to think of it is as five square layers. Each measures five cubes by five cubes.

So it is made up of twenty five cubes.

The top layer has that cross shaped hole, which takes away five cubes.

Twenty five take away five leaves twenty cubes in this layer.

In the second layer, the hole punched through the top meets the holes punched round the sides by the top of the cross shape.

Instead of five cubes being removed, there are another one, two, three, four.

Nine taken out in total.

Twenty five take away nine leaves sixteen cubes in this layer.

The middle layer is where the cross shaped holes are widest.

Another three cubes have been removed from each corner.

That leaves just four cubes in the middle layer.

The fourth layer is the same as the second, so it has sixteen cubes.

And the bottom layer is the same as the top so it has twenty cubes.

So the total number of individual cubes is twenty plus sixteen plus four plus sixteen plus twenty which equals seventy six.

How did you get on? Did you work it out?