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        

Four Cubes

Age 11 to 14 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

Age 11 to 14 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?

Multiplication Cube

Age 11 to 14 Short Challenge Level:

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

Dicey Directions

Age 11 to 14 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

Age 11 to 14 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

Age 11 to 14 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

Age 11 to 14 Short Challenge Level:

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

Net Result

Age 11 to 14 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?

Painted Octahedron

Age 11 to 14 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

Age 11 to 14 Short Challenge Level:

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

Rotation Identification

Age 11 to 14 Short Challenge Level:

Which of these can be obtained by rotating this shape?

Painted Purple

Age 11 to 14 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?

Daniel's Star

Age 11 to 14 Short Challenge Level:

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

Net Profit

Age 11 to 14 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?

Stacked Cubes

Age 11 to 14 Short Challenge Level:

What is the total surface area of this shape?

Facial Sums

Age 11 to 14 Short Challenge Level:

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

Red or Black

Age 11 to 14 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?

Truncated Tetrahedron

Age 11 to 14 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

Age 11 to 14 Short Challenge Level:

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

Cubic Covering

Age 11 to 14 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?

Blockupied

Age 11 to 14 Short Challenge Level:

Weekly Problem 28 - 2007
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

Pyramidal N-gon

Age 11 to 14 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?

Which Face?

Age 11 to 14 Short Challenge Level:

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

Magic Octahedron

Age 11 to 14 Short Challenge Level:

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

Twelve Cubed

Age 14 to 16 Short 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?