2D representations of 3D shapes

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

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

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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

Can you make a 3x3 cube with these shapes made from small cubes?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?