Shapes and symmetry
3D shapes
Look at a 3D shape from three directions and you get three flat pictures. Together they describe it completely.
Three views
You can describe a 3D shape by drawing what it looks like from three directions: TOP VIEW — looking straight down on it. FRONT VIEW — looking straight at the front. SIDE VIEW — looking straight at the side. Each view is a flat 2D drawing.
Prisms
A PRISM has the same cross-section all the way along. Its top view (looking down the length) shows that cross-section. So a hexagonal prism has a hexagon as its cross-section, a pentagonal prism a pentagon, and an octagonal prism an octagon. Counting the sides in that view names the prism.
The shape where all three views match
A CUBE looks the same from the top, the front and the side — a square every time. A SPHERE also has three identical views: a circle from every direction. Most shapes do not. A cylinder standing upright gives a circle from the top but a rectangle from the front and the side.
Reading a view back
Given three views you can often work out the shape. Three squares → a cube. Three circles → a sphere. A circle on top with rectangles at the front and side → a cylinder. A triangular prism gives a triangle from one direction and rectangles from the other two.
Worked examples
The three views of a cube
- Look from the top, the front and the side.
- Each is the same square.
Answer: Three identical squares
The three views of a sphere
- A sphere looks the same from every direction.
Answer: Three identical circles
The views of an upright cylinder
- From the top you see the circular end.
- From the front and side you see a rectangle.
Answer: A circle and two rectangles
Naming a prism from its cross-section
- A prism has the same cross-section all along.
- Count the sides in that view.
Answer: A hexagonal cross-section means a hexagonal prism
Three views: a triangle and two rectangles
- A triangular cross-section, rectangles along the length.
Answer: A triangular prism
Why draw three views at all?
- Each view is a flat 2D picture.
- Together they pin the solid down.
Answer: Three views describe the shape completely
Where you see this in real life
- Architects' plans are exactly this: a plan view from above plus elevations from the front and side.
- Flat-pack furniture instructions show a part from several directions because one picture is not enough to identify it.
Key words
- Top view
- what you see looking straight down
- Front view
- what you see looking straight at the front
- Side view
- what you see looking straight at the side
- Prism
- a 3D shape with the same cross-section all along its length
- Cross-section
- the shape you see when you cut straight through
- 3D shape
- a solid shape with length, width and height
- 2D shape
- a flat shape
- Face
- one flat surface of a solid