# 3D Shapes - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on 3D Shapes.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Stage 3 ★★ Sheet 1 Solutions Sheet 2 Solutions

### Painted Octahedron

##### KS 3 Short Challenge Level:

Weekly Problem 4 - 2014
What is the smallest number of colours needed to paint the faces of a regular octahedron so that no adjacent faces are the same colour?

### Cubic Vision

##### KS 3 Short Challenge Level:

Weekly Problem 1 - 2010
How many cubes can you see?

### Painted Purple

##### KS 3 Short Challenge Level:

Weekly Problem 18 - 2010
Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?

### Net Profit

##### KS 3 Short Challenge Level:

Weekly Problem 41 - 2015
The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube?

### Daniel's Star

##### KS 3 Short Challenge Level:

Weekly Problem 39 - 2007
A solid 'star' shape is created. How many faces does it have?

### Four Cubes

##### KS 3 Short Challenge Level:

Weekly Problem 11 - 2016
Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?

### Crawl Around the Cube

##### KS 3 Short Challenge Level:

Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?

### Dicey Directions

##### KS 3 Short Challenge Level:

Weekly Problem 25 - 2008
An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

### Same Face

##### KS 3 Short Challenge Level:

Weekly Problem 27 - 2017
A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?

### Sugary Diversion

##### KS 3 Short 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?

### Soma Surface

##### KS 3 Short Challenge Level:

Weekly Problem 48 - 2017
What is the surface area of the solid shown?

### Net Result

##### KS 3 Short Challenge Level:

Weekly Problem 5 - 2009
The net shown here is cut out and folded to form a cube. Which face is then opposite the face marked X?

### Red or Black

##### KS 3 Short Challenge Level:

Weekly Problem 1 - 2012
How many edges of a cube need to be coloured black to mean every face has at least one black edge?

### Pyramidal N-gon

##### KS 3 Short Challenge Level:

Weekly Problem 43 - 2014
The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?

### Cubic Covering

##### KS 3 Short Challenge Level:

Weekly Problem 31 - 2006
A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?

### Facial Sums

##### KS 3 Short Challenge Level:

Weekly Problem 41 - 2010
Can you make the numbers around each face of this solid add up to the same total?

### Truncated Tetrahedron

##### KS 3 Short Challenge Level:

Weekly Problem 2 - 2012
A tetrahedron has each corner cut off to produce a solid. What is the total length of the edges of this solid?

### Stretched Surfaces

##### KS 3 Short Challenge Level:

The edges of a cube are stretched, can you find the new surface area?

### Magic Octahedron

##### KS 3 Short Challenge Level:

Weekly Problem 20 - 2010
You have already used Magic Squares, now meet a Magic Octahedron...