Properties of 3D Shapes (CIE IGCSE Maths: Core)

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

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

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

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

• 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

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
  •  
• The width of the rectangle is equal to the height of the 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