Cuboid Challenge

Can you make this cuboid?

This activity is really easy to describe, but difficult to carry out! It is a very hands on activity that should help develop a really good understanding of the geometry of pyramids. Making them is the very best way of finding out about them! You may be required to use Pythagoras’s theorem and trigonometry to work out some missing lengths.


To provide an engaging context to explore the geometry of pyramids and prisms. In doing so, the aim is to gain understanding about these shapes and to practice skills such as working out missing lengths, volumes and surface areas. As such it is a great context for practice as well as discovery.

The Challenge

  • Make a cuboid that is 15cm, by 10cm by 5 cm from 3 different shapes.
  • The shapes must fit together to make the cuboid
  • No two of the shapes may be the same
  • No more than one of the shapes may be a prism!

Measurements and Calculations

  • Sketch the nets of the three shapes and calculate all of the missing lengths
  • Work out the area of all of the faces of the shapes.
  • Calculate the volume of the shapes and show that they are equal to volume of the cuboid – 750cm3
  • Identify which faces of the shapes will be on the outside of the cuboid when fitted together. Show that their combined surface area is 550cm²


The task can be displayed on this screen or given as the printed   Cuboid challenge activity sheet ​activity sheet.

Afterwards, classrooms will need a good supply of building materials, preferably card and tape!


​The ToK in this activity is about the reasoning needed to prove or disprove  a proposed solution. In order to make progress you need to establish facts (axioms) on which you can build in order to make further progress. As such this is a nice model of how mathematical knowledge can be built.

What, when and how?

Here are some thoughts for teachers about running this activity

  • It is very much up to the teacher to decide how open to make this task. I find it is at its best when you start with an open question and feed in little bits of help as and when required.
  • Encourage students to actually build the shapes. Even if they are not part of a correct solution, the process of making the shapes is when students really begin to make links.

A solution

Click on the hidden icon to see a couple of pictures of a solution


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