3D Shapes Short Problems: Age 11-16

This is part of our collection of Short Problems.

You may also be interested in our longer problems on 3D Shapes: Age 11-16.

We have put together a selection of these short problems as printable worksheets:

Printable worksheets: Age 11-14 ⭐   Printable worksheet: Age 11-14 ⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in turquoise pots.
    problem

    Daniel's Star

    Age
    11 to 14
    Challenge level

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

  • Small pepper seedlings in turquoise pots.
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Painted Octahedron

    Age
    11 to 14
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Soma Surface

    Age
    11 to 14
    Challenge level

    What is the surface area of the solid shown?

  • Small pepper seedlings in turquoise pots.
    problem

    Rotation Identification

    Age
    11 to 14
    Challenge level

    Which of these can be obtained by rotating this shape?

  • Small pepper seedlings in turquoise pots.
    problem

    Multiplication Cube

    Age
    11 to 14
    Challenge level

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

  • Small pepper seedlings in turquoise pots.
    problem

    Red or Black

    Age
    11 to 14
    Challenge level

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

  • Small pepper seedlings in turquoise pots.
    problem

    Blockupied

    Age
    11 to 14
    Challenge level

    A 1×2×3 block is placed on an 8×8 board and rolled several times.... How many squares has it occupied altogether?

  • Small pepper seedlings in turquoise pots.
    problem

    Truncated Tetrahedron

    Age
    11 to 14
    Challenge level

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

  • Small pepper seedlings in turquoise pots.
    problem

    Net Profit

    Age
    11 to 14
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Same Face

    Age
    11 to 14
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Magic Octahedron

    Age
    11 to 14
    Challenge level

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

  • Small pepper seedlings in turquoise pots.
    problem

    Crawl Around the Cube

    Age
    11 to 14
    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?

  • Small pepper seedlings in turquoise pots.
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Dicey Directions

    Age
    14 to 16
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Four Cubes

    Age
    14 to 16
    Challenge level

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

  • Small pepper seedlings in turquoise pots.
    problem

    Which Face?

    Age
    14 to 16
    Challenge level

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

  • Small pepper seedlings in turquoise pots.
    problem

    Stacked Cubes

    Age
    14 to 16
    Challenge level

    What is the total surface area of this shape?

  • Small pepper seedlings in turquoise pots.
    problem

    Cubic Covering

    Age
    14 to 16
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Cubic Vision

    Age
    14 to 16
    Challenge level

    How many cubes can you see?

  • Small pepper seedlings in turquoise pots.
    problem

    Painted Purple

    Age
    14 to 16
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Facial Sums

    Age
    14 to 16
    Challenge level

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

  • Small pepper seedlings in turquoise pots.
    problem

    Pyramidal N-Gon

    Age
    14 to 16
    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Stretched Surfaces

    Age
    14 to 16
    Challenge level

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

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