# 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.