3D Shapes | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Properties of 3D Shapes

In this section, we will explore the characteristics of various 3D shapes, focusing on their faces, symmetry planes, and unique properties.

What 3D shapes should I know?

• Acquire familiarity with the general designations of prisms, which are 3D shapes featuring uniform cross-sections.
• The cross-section of a cube forms a square, while that of a cuboid creates a rectangle. Similarly, a cylinder's cross-section is circular.
• Be prepared to deal with various prisms in assessments, including triangular prisms, with clear indication of the cross-sectional shape provided in the question.
• Understand the nomenclature and attributes of different types of pyramids.
  • Pyramids possess a flat base and sloping sides converging at a single point.
  • The base is typically a 2D shape, and many pyramids derive their names from the shape of their base, such as a square-based pyramid.
  • Certain pyramids have unique appellations that warrant recognition.
  • Examples include cones with circular bases and tetrahedrons featuring equilateral triangle bases.
• Learn about spheres, their name, and properties.

What are the properties of 3D shapes?

• 3D shapes are characterized by their faces, vertices, and edges.
• Each face represents an individual surface of the 3D shape.
• Vertices (plural, vertices) denote the corners of the 3D shape.
• Edges connect one vertex to another.
• Understanding the number and shape of faces is crucial for common 3D shapes.
  • A cube boasts 6 equal square faces.
  • A cuboid features 3 pairs of equal rectangular faces.
  • A cylinder comprises two equal circular faces and one rectangular face, which is its curved surface area.
  • A triangular prism has two equal triangular faces and three rectangular faces.
• In cases where triangular faces are equilateral, all rectangles will be equal.
• If triangular faces are isosceles, two rectangles will be equal.
• A square-based pyramid possesses one square face and four equal triangular faces.
• A tetrahedron consists of four triangular faces.
• 3D shapes can be unfolded into a net to exhibit their 2D faces.
• A net is essentially a pattern that, when folded, forms the 3D shape.