3D Shapes

For Elementary Students

What is a 3D Shape?

A 3D shape (three-dimensional shape) is a shape that has length, width, and height. You can hold it in your hands!

Think about it like this:

• A circle on paper is flat (2D)
• A ball is round all around and takes up space (3D)

3D shapes are also called solids.

Common 3D Shapes

Cube

A cube has 6 square faces (like a box with all sides equal).

Features:

• 6 faces (all squares, all the same size)
• 12 edges (where two faces meet)
• 8 corners (also called vertices)

Examples in real life:

• Dice
• Rubik's Cube
• Ice cube
• Gift box (if it's a perfect cube)

Sphere

A sphere is perfectly round, like a ball.

Features:

• No flat faces
• No edges
• No corners
• Every point on the surface is the same distance from the center

Examples in real life:

• Basketball
• Globe
• Orange
• Marble

Cylinder

A cylinder has two flat circular ends and one curved surface.

Features:

• 2 circular faces (top and bottom)
• 1 curved surface (the side)
• 2 edges (where the circles meet the curved surface)

Examples in real life:

• Soda can
• Toilet paper roll
• Battery
• Jar

Cone

A cone has one flat circular base and comes to a point at the top.

Features:

• 1 circular face (the bottom)
• 1 curved surface (the side)
• 1 edge (where the circle meets the curved part)
• 1 vertex (the point at the top)

Examples in real life:

• Ice cream cone
• Party hat
• Traffic cone
• Funnel

Rectangular Prism

A rectangular prism looks like a box.

Features:

• 6 faces (all rectangles; opposite faces are the same)
• 12 edges
• 8 vertices

Examples in real life:

• Cereal box
• Book
• Brick
• Tissue box

Pyramid

A pyramid has a base (usually square) and triangular sides that meet at a point.

Features:

• 5 faces (1 square base + 4 triangular sides)
• 8 edges
• 5 vertices

Examples in real life:

• Egyptian pyramids
• Pyramid building toys
• Some tents

For Junior High Students

Faces, Edges, and Vertices

All 3D shapes (except spheres) are made of:

• Faces — the flat surfaces
• Edges — where two faces meet (the lines)
• Vertices (singular: vertex) — where edges meet (the corners)

Prisms

A prism is a 3D shape with:

• Two identical ends (bases)
• Flat rectangular sides connecting the bases

Types of prisms:

• Rectangular prism (bases are rectangles)
• Triangular prism (bases are triangles — like a Toblerone bar)
• Pentagonal prism (bases are pentagons)

The shape is named by the shape of its base.

Euler's Formula

For many 3D shapes, there's a relationship between faces (F), vertices (V), and edges (E):

F + V = E + 2

Example: Cube

• F = 6 faces
• V = 8 vertices
• E = 12 edges

Check: 6 + 8 = 12 + 2 → 14 = 14 ✓

This works for prisms and pyramids!

Volume and Surface Area (Preview)

With 3D shapes, we can calculate:

• Volume — how much space is inside (measured in cubic units like cm³)
• Surface Area — the total area of all the faces (measured in square units like cm²)

We will learn how to calculate these later.

Cross Sections

If you slice a 3D shape, the flat surface you create is called a cross section.

Example:

• Slice a cylinder horizontally → you get a circle
• Slice a cube diagonally → you might get a rectangle or triangle

Nets

A net is a flat pattern that can be folded to make a 3D shape.

Example: Cube net

  +---+
  | T |
+---+---+---+---+
| L | F | R | B |
+---+---+---+---+
  | Bt|
  +---+

(T=top, L=left, F=front, R=right, B=back, Bt=bottom)

Fold along the edges and you get a cube!

We will learn more about nets later.

Practice