# 3D Shapes, Nets and Views

> Name prisms, pyramids, cylinders, cones and spheres, count faces, edges and vertices, fold nets, and draw the top, front and side views of a solid.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/solids-nets-and-views/. Updated 4 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The tissue box
Leo flattens an empty tissue box to put in the recycling. He pulls the glued flap open and lays the cardboard flat. It is a strange cross shape made of six rectangles.

"That flat shape is called a net," his sister Zara says. "Fold it up and you get the box back. The box has 6 faces, 12 edges and 8 corners."

Leo turns the box and looks at it from the top, then the front, then the side. Each time he sees a different rectangle. "So one shape can look like three different flat pictures," he says.

**In short:** A 3D shape has faces (flat sides), edges (where two faces meet) and vertices (corners). Prisms have the same shape all the way through, and pyramids come to a point. A net is the flat pattern that folds into the solid, and the top, front and side views are what you see from each direction.

## Before you start

- The names of 2D shapes: triangle, square, rectangle, pentagon, hexagon, circle (see Triangles and Quadrilaterals).

## Faces, edges and vertices

### Key idea: Three words
- A **face** is a flat surface.
- An **edge** is a line where two faces meet.
- A **vertex** is a corner where edges meet. The plural is **vertices**.

## Prisms and pyramids

A **prism** has two matching ends joined by rectangles. Cut it anywhere parallel to the end and you get the same shape. A **pyramid** has one base, and triangles that meet at a point called the apex.

Both are named after their base.

| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Rectangular prism | 6 | 12 | 8 |
| Triangular prism | 5 | 9 | 6 |
| Hexagonal prism | 8 | 18 | 12 |
| Square pyramid | 5 | 8 | 5 |
| Triangular pyramid | 4 | 6 | 4 |

### Exam tip: A check that always works
For a prism or a pyramid, faces $+$ vertices $-$ edges $= 2$.

Cube: $6 + 8 - 12 = 2$. Square pyramid: $5 + 5 - 8 = 2$.

### Key idea: Shortcuts for a base with n sides
- Prism: $n + 2$ faces, $3n$ edges, $2n$ vertices.
- Pyramid: $n + 1$ faces, $2n$ edges, $n + 1$ vertices.

## Curved solids

- A **cylinder** has two flat circle faces and one curved surface, like a can.
- A **cone** has one flat circle face, one curved surface and one point at the top, like an ice cream cone.
- A **sphere** has one curved surface and no flat faces, like a ball.

## Nets

A **net** is a flat shape that folds up into a solid. A cube has 11 different nets. Here is one.

*Diagram: A cross shaped net of a cube: square A on top, a row of four squares B, C, D and E in the middle, and square F below C*
*Fold this net into a cube. A and F end up opposite each other, and so do B and D, and C and E.*

### Exam tip: Opposite faces in a net
In a straight row of squares, faces that are **one square apart** are opposite. B and D are opposite, and so are C and E. Two faces that touch in the net can never be opposite.

A triangular prism's net has 2 triangles and 3 rectangles. A square pyramid's net has 1 square and 4 triangles.

## Views from the top, front and side

Imagine looking straight at a solid from one direction. You see a flat shape called a **view**.

| Solid | Top view | Front view | Side view |
|---|---|---|---|
| Cylinder standing up | Circle | Rectangle | Rectangle |
| Cone standing on its base | Circle with a dot in the middle | Triangle | Triangle |
| Square pyramid | Square with lines to the centre | Triangle | Triangle |
| Sphere | Circle | Circle | Circle |

A **shadow** works the same way. Shine a torch straight down on a standing can and its shadow is a circle. Shine it from the side and the shadow is a rectangle.

A **cross-section** is the face you get by cutting straight through a solid. Cut a prism parallel to its end and the cross-section is the same shape as the end.

### Challenge: Selective level: painted cubes and stacks
A $3 \times 3 \times 3$ cube made of 27 small cubes is painted on the outside, then pulled apart.

- The 8 corner cubes have 3 painted faces.
- Each of the 12 edges has 1 middle cube with 2 painted faces: 12 cubes.
- Each of the 6 faces has 1 centre cube with 1 painted face: 6 cubes.
- The 1 cube in the very middle has no paint. Check: $8 + 12 + 6 + 1 = 27$.

A solid has 7 faces and 10 vertices. Faces $+$ vertices $-$ edges $= 2$, so $7 + 10 - \text{edges} = 2$ and it has 15 edges. It is a pentagonal prism.

**Mind map**

```text
3D shapes
  Parts
    Faces are flat
    Edges where faces meet
    Vertices are corners
  Solids
    Prisms: same all through
    Pyramids: come to a point
    Cylinder, cone, sphere
  Rules
    F + V - E = 2
    Name by the base
  Nets
    Fold into the solid
    One apart in a row: opposite
  Views
    Top, front, side
    Shadows and cross-sections
```

## Quick summary

- Faces are flat, edges are where faces meet, vertices are corners.
- Prisms and pyramids are named after their base.
- For prisms and pyramids, faces $+$ vertices $-$ edges $= 2$.
- A cube has 6 faces, 12 edges and 8 vertices.
- A net folds into a solid. In a row of squares, faces one apart are opposite.
- The top, front and side views are what you see looking straight at each side.

## Quiz

Try these questions from the chapter quiz.

1. How many faces does a cube have?
   - A. 4
   - B. 6
   - C. 8
   - D. 12
   - Answer: B. 6. A cube has 6 square faces, like a dice.

2. Which solid has one curved surface and no flat faces?
   - A. Cylinder
   - B. Cone
   - C. Sphere
   - D. Cube
   - Answer: C. Sphere. A sphere, like a ball, has only a curved surface.

3. Which solid has 4 faces, 6 edges and 4 vertices?
   - A. Square pyramid
   - B. Triangular pyramid
   - C. Triangular prism
   - D. Cube
   - Answer: B. Triangular pyramid. A triangular pyramid has a triangle base and 3 triangle sides.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/solids-nets-and-views/#quiz