### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# 3D Shapes

Three-dimensional (3D shapes), as the name implies, are shapes that have depth in addition to height and width. This feature makes them different from 2D shapes, which are flat and only have two dimensions – length and width.

Before we look at 3D shapes, let’s take a quick detour back to 2D shapes, which can be considered the ‘blueprints’ for 3D shapes. For example, when you stretch a square (a 2D shape) along its depth, you get a cube (a 3D shape). The same principle applies to a circle forming a sphere, or a triangle extending into a pyramid.

Now, it’s useful to familiarise yourself with some common terms associated with 3D shapes:

• Face – A flat or curved surface of a 3D shape
• Edge – The line segment where two faces of a 3D shape meet
• Vertex – The point where two or more edges meet
• Base – The surface a shape is resting on
• Height – The vertical distance from the base to the top of the shape
• Cross section – The shape we get when cutting straight through an object

## Types of 3D Shapes

There are many different types of 3D shapes. Let’s look at some that you’re expected to know.

• Cube – A cube is a six-faced shape with all faces being square and meeting at right angles. Each face has equal dimensions, so all edges are the same length. An example of a cube in real life is a dice.
• Cuboid – A cuboid, also known as a rectangular prism, resembles a stretched or flattened cube. It has six faces, with opposite faces being equal, but not all edges have to be the same length. A real-life example of a cuboid is a brick.

• Sphere – A sphere is perfectly symmetrical around its centre, with all points on the surface equidistant (equal distances) from the centre. It has one continuous curved face.
• Cone – A cone has a circular base and a vertex opposite the base. The base is flat, while the rest of the shape forms a curved surface.
• Cylinder – A cylinder has two parallel circular bases of equal size and a curved surface connecting the bases.

• Square-based Pyramid – As the name suggests, this pyramid has a square base with four triangular faces meeting at a common vertex.
• Tetrahedron – This shape, also known as a triangular pyramid, has four triangular faces, all meeting at a common point.

• Triangular Prism – This shape has two triangular bases of equal size and three rectangular faces.
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