Properties of 3D Shapes (Cambridge (CIE) IGCSE Maths) : Revision Note

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

Volume of a prism
Volume of a cylinder
  • 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 triangular-based pyramid is called a tetrahedron

    • A cone is similar to a pyramid

      • A cone has a circular base

Volume of a pyramid
Cone volume, IGCSE & GCSE Maths revision notes
  • You should know the name and properties of a sphere

Sphere Radius r, IGCSE & GCSE Maths revision notes

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 Tips and Tricks

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

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Jamie Wood

Author: Jamie Wood

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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.

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Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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