3D shapes and their properties

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Volume of a Pyramid and a Cone

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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Mouhefanggai

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
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Thinking 3D

How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?
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Paper folding - models of the Platonic solids

A description of how to make the five Platonic solids out of paper.
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Let's Get Flexible with Geometry

In this article for primary teachers, Ems explores ways to develop mathematical flexibility through geometry.
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Going Deeper: Achieving Greater Depth with Geometry

This article for Primary teachers outlines how providing opportunities to engage with increasingly complex problems, and to communicate thinking, can help learners 'go deeper' with geometry.
problem

Four Points on a Cube

Age

16 to 18

Challenge level

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?
problem

Construct-o-straws

Age

7 to 11

Challenge level

Make a cube out of straws and have a go at this practical challenge.
problem

Cereal Packets

Age

7 to 11

Challenge level

How can you put five cereal packets together to make different shapes if you must put them face-to-face?
problem
Favourite

Hamiltonian Cube

Age

11 to 16

Challenge level

Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.