What is an orthographic view?
Imagine looking at a solid from very far away, straight on, so that all lines of sight are parallel. What you see is a flat outline. This is an orthographic view (ortho = straight, graphic = drawing).
- Front view (front elevation): seen from the front. Shows width and height.
- Top view (plan): seen from above. Shows width and depth.
- Side view (side or end elevation): seen from the left or right. Shows depth and height.
Each view hides one measurement, so one view is not enough. For a solid made of cubes, the front view shows the tallest stack in each column; the top view shows which squares are covered.
From views back to the solid
To rebuild a solid from its views:
- Use the top view to mark which squares on the base have cubes.
- Use the front view to find the greatest height in each column.
- Use the side view to find the greatest height in each row.
- A stack can be no taller than both limits allow. Fill in heights that match all three views.
Sometimes more than one solid fits the same views. Then you can find the least and greatest number of cubes possible.
Layout: first-angle and third-angle projection
Technical drawings place the views in a fixed pattern so anyone can read them.
- First-angle projection (India, Europe, ISO): the plan is drawn below the front view; the view from the left is drawn on the right.
- Third-angle projection (USA, Canada): the plan is drawn above the front view; the view from the right is drawn on the right.
A small symbol (a truncated cone shown in two views) tells you which method is used.
Lines and dimensions
- Thick continuous line: visible edge.
- Thin dashed line: hidden edge.
- Thin chain line (long dash, short dash): centre line or axis of symmetry.
- Dimensions are written in millimetres, on thin lines with arrowheads, placed outside the view; each size is given once.
Nets and cross-sections
A net is a flat shape that folds up into a solid.
- A cube has 11 different nets, each with 6 squares.
- A cuboid net has 6 rectangles in 3 matching pairs.
- A triangular prism: 2 triangles and 3 rectangles.
- A cylinder: 2 circles and 1 rectangle whose length is the circumference 2πr.
- A cone: 1 circle and a sector of a circle.
A cross-section is the flat face you get when a plane cuts a solid. A prism cut parallel to its end gives the same shape as the end. A cylinder cut straight across gives a circle; cut along its length, a rectangle. A cube can even give a triangle or a hexagon if cut at a slant. In technical drawing a sectional view shows the cut face with thin slanted lines (hatching).
Try it: draw a matchbox
Take a matchbox or any small box. Put it on the table. Draw what you see from the front, from above and from the right, each as a flat rectangle, and arrange them in first-angle layout. Measure and add dimensions in mm. Then open the box flat and draw its net. In the 3D free-play step, change stacks and predict the views before you press the button.
Key formulas and definitions
- Front view = width × height; top view = width × depth; side view = depth × height
- Cube solid: front view height of a column = tallest stack in that column
- First angle: plan below elevation; third angle: plan above elevation
- Cylinder net: rectangle length = 2πr, width = h; plus 2 circles
- Cube has 11 nets; every net has 6 squares
Worked examples
1. A solid has stacks of heights (back row) 1, 0, 0; (middle row) 2, 1, 0; (front row) 3, 2, 1. Draw the front view.
For each column take the tallest stack. Column 1: max(1, 2, 3) = 3. Column 2: max(0, 1, 2) = 2. Column 3: max(0, 0, 1) = 1. The front view is three columns of 3, 2 and 1 squares: a staircase.
2. For the same solid, how many squares are in the top view and how many cubes are there?
Covered squares: back row 1, middle 2, front 3 = 6 squares in the top view. Cubes: 1 + 2 + 1 + 3 + 2 + 1 = 10 cubes.
3. A cylinder has radius 7 cm and height 10 cm. Find the size of the rectangle in its net. (π = 22/7)
Length = circumference = 2πr = 2 × 22/7 × 7 = 44 cm. Width = height = 10 cm. So the rectangle is 44 cm × 10 cm, plus two circles of radius 7 cm.
4. The top view of a cube solid is a 2 × 2 square. The front view shows heights 2 and 1; the side view shows heights 2 and 1. What are the least and the greatest number of cubes?
Greatest: each stack takes the smaller of its column and row limits: 2, 1, 1, 1 = 5 cubes. Least: put a 2-stack where the tall column meets the tall row and 1s elsewhere so every square is covered: 2 + 1 + 1 + 1 = 5. Here both equal 5 cubes.
Common mistakes
- Adding heights in a column for the front view. The front view shows only the tallest stack in each column, not the sum.
- Mixing first- and third-angle layouts. Check the symbol: in first angle the plan is below.
- Drawing hidden edges as solid lines. Hidden edges are dashed.
- Forgetting that a cylinder net's rectangle length is the circumference 2πr, not the diameter.