3D shapes and their properties

There are 49 NRICH Mathematical resources connected to 3D shapes and their properties
Auditorium Steps
problem

Auditorium steps

Age
7 to 14
Challenge level
filled star filled star filled star
What is the shape of wrapping paper that you would need to completely wrap this model?
Four Points on a Cube
problem

Four points on a cube

Age
16 to 18
Challenge level
filled star empty star empty star
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?
Dodecawhat
problem

Dodecawhat

Age
14 to 16
Challenge level
filled star empty star empty star

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

Volume of a Pyramid and a Cone
article

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.
Mouhefanggai
article

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.
Thinking 3D
article

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?