3D Geometry, Shape and Space - June 2004, Stage 2&3

Problems

problem icon

Building Blocks

Stage: 2 Challenge Level: Challenge Level:1

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

problem icon

Right or Left?

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these dice are right-handed and which are left-handed?

problem icon

A Chain of Eight Polyhedra

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

problem icon

Cut Nets

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

problem icon

Painted Cube

Stage: 3 Challenge Level: Challenge Level:1

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

problem icon

Triangles to Tetrahedra

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

problem icon

Tetrahedra Tester

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?