# Geometry of 3D Shapes

## Geometry of 3D Shapes

### Understanding 3D Shapes

• Familiarise yourself with the common 3D shapes: cube, cuboid, cylinder, cone, sphere, pyramid, and prism.
• Learn the formulas for the volume and surface area of these shapes and be able to apply them.
• Understand how to identify each of these unique shapes based on their properties: edges, vertices, and faces.

### Polyhedra

• Comprehend the definition and characteristics of polyhedra, which are 3D shapes with flat faces.
• A polyhedron has a definite number of faces, edges, and vertices. Familiarise yourself with how these quantities relate to each other (Euler’s formula: Faces + Vertices - Edges = 2).
• Identify the difference between regular and irregular polyhedra. Regular polyhedra, also known as Platonic solids, have faces that are regular polygons of the same size and shape.

### Surface Area and Volume

• Recognize the surface area of a 3D shape as the total area of all its outside surfaces.
• Know how to calculate the surface area of a shape, typically by finding the area of each face and adding them together.
• Understand volume as the quantity of 3D space enclosed by a closed surface.
• Learn and apply the formulas for finding the volume of a shape.

### Sphere, Cylinder and Cone

• Realize that the formulas are different when it comes to a sphere, cylinder, and cone due to their curved surfaces.
• For a sphere, memorise and understand how to apply the formulas for surface area (4πr²) and volume (4/3πr³).
• With a cylinder, be able to calculate the surface area (2πr(r + h)) and volume (πr²h) accurately.
• Whereas for a cone, familiarise yourself with the formulas for surface area (πr(r + l)) and volume (1/3πr²h), where l represents the slant height.

### Cross Sections

• Understand the concept of cross sections, which are the shapes you get when you slice through a 3D shape.
• Be able to identify the cross section of different 3D shapes, and how the position of the slice can change the resulting cross section.
• Know the difference between horizontal and vertical cross sections.

### Practical Applications

• Apply all these principles to solve real-world problems that involve 3D shapes — for instance, in packaging, construction or design-related challenges.
• Combine 3D shape understanding with other mathematical concepts, such as ratios or algebra, for complex problem-solving.