Cubes and cuboids

problem
Classifying solids using angle deficiency

Age

11 to 16

Challenge level

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
problem
Classic cube

Age

16 to 18

Challenge level

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?
problem
Twelve cubed

Age

14 to 16

Challenge level

A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?
problem
Sugary diversion

Age

11 to 14

Challenge level

Weekly Problem 48 - 2008
An ant is crawling in a straight line when he bumps into a one centimetre cube of sugar.If he climbs over it before before continuing on his intended route, how much does the detour add to the length of his journey?
problem
Net result

Age

11 to 14

Challenge level

The net shown here is cut out and folded to form a cube. Which face is then opposite the face marked X?
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
Tic tac toe

Age

11 to 14

Challenge level

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
problem
All tied up

Age

14 to 16

Challenge level

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
problem
Inside out

Age

14 to 16

Challenge level

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you can colour every face of all of the smaller cubes?