3D shapes and their properties

  • Hamiltonian Cube
    problem
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    Hamiltonian Cube

    Age
    11 to 16
    Challenge level
    filled star filled star empty star
    Weekly Problem 36 - 2007
    Find the length along the shortest path passing through certain points on the cube.
  • Building with Solid Shapes
    problem
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    Building With Solid Shapes

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

  • Skeleton Shapes
    problem
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    Skeleton Shapes

    Age
    5 to 7
    Challenge level
    filled star filled star empty star

    How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

  • Shadow Play
    problem
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    Shadow Play

    Age
    5 to 7
    Challenge level
    filled star filled star filled star

    Here are shadows of some 3D shapes. What shapes could have made them?

  • Cubes
    problem
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    Cubes

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    How many faces can you see when you arrange these three cubes in different ways?
  • Building Blocks
    problem
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    Building Blocks

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

  • Guess What?
    problem
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    Guess What?

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Can you find out which 3D shape your partner has chosen before they work out your shape?

  • Sponge Sections
    problem
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    Sponge Sections

    Age
    7 to 11
    Challenge level
    filled star filled star empty star

    You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

  • Cut Nets
    problem
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    Cut Nets

    Age
    7 to 11
    Challenge level
    filled star filled star empty star

    Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?