3D Shapes (Edexcel GCSE Maths: Foundation)

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Jamie W

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Jamie W

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Properties of 3D Shapes

What are the names of common 3D shapes?

  • You should know the general names of prisms
    • A prism is a 3D shape with the same cross-section throughout
      • The cross-section of a cube is a square
      • The cross-section of a cuboid is a rectangle
    • You will also have to work with other prisms, such as triangular prisms or hexagonal prisms
      • In these cases the exam question will make sure the shape of the cross-section is clear
    • A cylinder is similar to a prism
      • The cross-section of a cylinder is a circle
  • You should know the names and properties of the different types of pyramids
    • A pyramid has a flat base with sloping sides that meet at a point at the top
    • A square–based pyramid has a square as its base
    • Some pyramids have special names you should know
      • A tetrahedron’s base is an equilateral triangle
    • A cone is similar to a pyramid
      • A cone has a circular base
  • You should know the name and properties of a sphere

What are the properties of 3D shapes?

  • 3D shapes have a number of faces, vertices and edges
    • A face is a single surface of the 3D shape
    • A vertex (plural, vertices) is a corner of the 3D shape
    • An edge joins one vertex to another
  • You should know the number and shape of the faces for the common 3D shapes
    • A cube has 6 equal, square faces
    • A cuboid has 3 pairs of rectangular faces
    • A cylinder has 2 equal circular faces and 1 rectangular face (its curved surface)
    • A triangular prism has 2 equal triangular faces and 3 rectangular faces
      • If the triangular faces are equilateral then all of the rectangles will be equal
      • If the triangular faces are isosceles then two of the rectangles will be equal
    • A square-based pyramid has 1 square face and 4 equal triangular faces
    • A tetrahedron has 4 triangular faces
    • A sphere has 1 face; it is a ball-shape

Properties of 3D shapes

Examiner Tip

  • Remembering the properties of 3D shapes will help in particular with questions involving surface area

Nets of Solids

What is a net of a solid?

  • A net of a solid is a 2D drawing that can be cut out and folded to make a 3D shape
  • Each of the faces of the 3D shape are arranged in a certain pattern
    • Not every arrangement of the faces will create a net of that solid   
    • Solids can have more than one arrangement that will work to make the 3D shape
  • The area of the net of a 3D shape is the same as the surface area of the solid

Nets of 3D shapes

What does the net of a cube or cuboid look like?

  • The net of a cube has 6 squares connected at certain edges
  • There are 11 different arrangements of the square faces that will form a net of a cube

Nets of a cube

  • The most common and easiest to remember is in the form of a cross

Cross shaped net of a cube

  • A cuboid has 6 rectangular faces, so its net consists of 6 rectangles
  • The rectangles will be in three pairs of two 
  • There are 54 different possible nets of a cuboid
    • Again, the most common and easiest to remember is in the form of a cross
    • Pay attention to which rectangles are the same
      • They are colour-coded in the diagram below

cross shaped net of a cuboid

What does the net of a cylinder look like?

  • The net of a cylinder consists of two circles and a rectangle
  • The length of the rectangle is equal to the circumference of the circles
    • Circumference equals space 2 cross times straight pi cross times radius 
  • The width of the rectangle is equal to the height of the cylinder


Net of a cylinder

What does the net of a pyramid look like?

  • The net of a square-based pyramid consists of one square and four congruent (identical) triangles
    • The perpendicular height of each triangle is equal to the slant height of the pyramid

Net of a pyramid

Examiner Tip

  • You may be given the dimensions of the solid when asked to draw a net
    • Make sure you put the correct lengths in the correct places by imagining cutting out and folding up the net

Worked example

A cuboid measures 6 cm by 3 cm by 2 cm.

On the 1 cm2 grid, draw an accurate net of this cuboid. One face has been drawn for you.
Net worked example question

The cuboid has three pairs of rectangles; measuring 6 cm by 3 cm, 6 cm by 2 cm, and 3 cm by 2 cm

Make sure the net has two of each of these rectangles in the correct places

Net worked example solution

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Jamie W

Author: Jamie W

Expertise: Maths

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.