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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# 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:

### Daniel's Star

### Multiplication Cube

### Net Result

### Painted Octahedron

### Rotation Identification

### Net Profit

### Same Face

### Truncated Tetrahedron

### Red or Black

### Blockupied

### Magic Octahedron

### Crawl Around the Cube

### Four Cubes

### Twelve Cubed

### Dicey Directions

### Which Face?

### Facial Sums

### Stretched Surfaces

### Cubic Covering

### Pyramidal N-gon

### Painted Purple

## You may also like

### Seven Squares - Group-worthy Task

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

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 â˜… | Sheet 1 | Solutions | Stage 3 â˜…â˜… | Sheet 1 | Solutions | |

Sheet 2 | Solutions |

Age 11 to 14

ShortChallenge Level

A solid 'star' shape is created. How many faces does it have?

Age 11 to 14

ShortChallenge Level

The net shown is folded up to form a cube. What is the largest possible vertex product?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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?

Age 11 to 14

ShortChallenge Level

Which of these can be obtained by rotating this shape?

Age 11 to 14

ShortChallenge Level

The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube?

Age 11 to 14

ShortChallenge Level

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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

Age 11 to 14

ShortChallenge Level

Weekly Problem 20 - 2010

You have already used Magic Squares, now meet a Magic Octahedron...

Age 11 to 14

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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?

Age 14 to 16

ShortChallenge Level

Which faces are opposite each other when this net is folded into a cube?

Age 14 to 16

ShortChallenge Level

Can you make the numbers around each face of this solid add up to the same total?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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?

Age 14 to 16

ShortChallenge Level

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?

Age 14 to 16

ShortChallenge Level

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?

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?