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        

Rotation Identification

Age 11 to 14 Short Challenge Level:

Which of these can be obtained by rotating this shape?

Daniel's Star

Age 11 to 14 Short Challenge Level:

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

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?

Soma Surface

Age 11 to 14 Short Challenge Level:

What is the surface area of the solid shown?

Net Result

Age 11 to 14 Short Challenge Level:

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:

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?

Blockupied

Age 11 to 14 Short Challenge Level:

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

Net Profit

Age 11 to 14 Short Challenge Level:

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

Same Face

Age 11 to 14 Short Challenge 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?

Truncated Tetrahedron

Age 11 to 14 Short Challenge Level:

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

Red or Black

Age 11 to 14 Short Challenge Level:

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

Magic Octahedron

Age 11 to 14 Short Challenge Level:

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

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?

Which Face?

Age 14 to 16 Short Challenge Level:

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

Stacked Cubes

Age 14 to 16 Short Challenge Level:

What is the total surface area of this shape?

Four Cubes

Age 14 to 16 Short Challenge Level:

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

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?

Dicey Directions

Age 14 to 16 Short Challenge 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?

Cubic Covering

Age 14 to 16 Short Challenge 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?

Pyramidal N-gon

Age 14 to 16 Short Challenge 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?

Painted Purple

Age 14 to 16 Short Challenge 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?

Facial Sums

Age 14 to 16 Short Challenge Level:

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

Stretched Surfaces

Age 14 to 16 Short Challenge Level:

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

Cubic Vision

Age 14 to 16 Short Challenge Level:

How many cubes can you see?