3D Shapes (Cambridge International IGCSE Maths)

Properties of 3D Shapes

What common 3D shapes do I need to know about?

• There are a number of common 3D shapes

  • You should know their names
  • and their key properties

• 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

  • There are 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

• There are a number of different types of pyramid

  • A pyramid has a flat base and sloping sides that meet at a point

  • The pyramid may have a square, rectangular or triangular base

  • Some pyramids have special names you should know

    • A triangular-based pyramid is called a tetrahedron

  • A cone is similar to a pyramid

    • A cone has a circular base

• A sphere is a round solid ball shape

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

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