Free printable resources · Original practice
Turn 12 original block models into front, top and right views. An explicit height plan removes hidden-cube guesswork; each solution shows the exterior silhouettes.
The complete collection
Download the student pack for practice and the separate answer pack to compare. Individual editable sheets appear below. The paper-size choice applies to every download button.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
Original practice with a separate reference answer. Choose Letter or A4.
| OR06 model | Exact result |
|---|---|
| Column heights, y = 0 | 3, 2, 1 |
| Front silhouette heights, x increasing | 3, 2, 1 |
| Right silhouette heights, y increasing | 3 |
| Top occupied footprint | Three cells in one row |
The front observer looks from negative y toward positive y. The right observer looks from positive x toward negative x, so y increases rightward in that view. The top view places the front edge at its bottom and y increases upward. In this third-angle exercise, top sits above front, and right sits to the right of front.
Begin by orienting the model so the front face is visible from negative y toward positive y. The x-axis increases to the right, defining the horizontal span of your drawing. For each column position along the x-axis, determine the maximum height across all y-values. This maximum value dictates the vertical extent of the silhouette at that specific x-coordinate. Draw only the outer boundary of this profile. Do not include internal seams or hidden edges, as these are deliberately omitted for beginning exercises. The resulting shape represents the front elevation, showing the tallest stack at each horizontal position without revealing depth details behind the frontmost cubes.
Rotate your perspective to view the model from positive x toward negative x. In this third-angle layout, the right view is placed to the right of the front view. The y-axis increases to the right on this specific view sheet. For each column position along the y-axis, calculate the maximum height across all x-values. This maximum determines the vertical height of the silhouette at that y-coordinate. Draw the outer boundary only, ignoring internal structures. This profile reveals the tallest stack at each depth position, providing a clear side elevation that complements the front view without showing hidden edges or internal seams.
Position the top view above the front view according to third-angle projection rules. On the sheet, x increases to the right and y increases upward, with the front edge located at the bottom. Identify every grid position where a solid stack exists from z=0. Draw the outline of these occupied positions to create the top footprint. This view shows the horizontal layout of the columns. Do not draw height indicators or hidden lines. The footprint confirms which x and y coordinates contain at least one cube. This simple outline helps verify the base area and aligns with the silhouettes generated in the front and right views for a complete spatial understanding.
| Watch for | Check instead |
|---|---|
| Drawing internal seams between adjacent columns in the front or right views. | Omit internal seams and hidden edges entirely. Draw only the outer silhouette of the maximum heights for each column position. |
| Placing the top view below the front view or misaligning the axes. | Place the top view above the front view. Ensure x increases to the right and y increases upward on the top view sheet. |
| Using average heights instead of maximum heights for the front and right profiles. | Calculate the maximum height over all y-values for the front view and over all x-values for the right view to define the silhouette. |
Before you begin
Internal seams and hidden edges are deliberately omitted for these beginning exercises. The focus is on drawing the outer silhouettes and top footprint only, simplifying the visual interpretation of the solid stacks.
For the front view, take the maximum height across all y-values for each x-position. For the right view, take the maximum height across all x-values for each y-position. This defines the silhouette.
The top view shows the footprint of the model. It outlines every grid position where a solid stack exists from z=0, indicating which x and y coordinates are occupied without showing vertical height.
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Fix the axes first. Let x run left to right, y run front to back, and z run bottom to top, with one unit cube per cell. A front view looks along y, so its horizontal coordinate is x and its vertical coordinate is z. A right view looks along x, so its horizontal coordinate is y and its vertical coordinate is z. A top view looks along z, so its horizontal coordinate is x and its vertical coordinate is y.
For each view, mark a cell as filled when at least one cube occupies the line of sight through that cell. This produces an occupancy silhouette. It does not tell you whether an internal edge would be visible or hidden in a finished line drawing, so keep those claims out of the exercise unless the model itself defines them.
Use eight unit cubes: six fill a 3 by 2 base at z = 0, with x = 0, 1, 2 and y = 0, 1. Add two cubes above the left column at (0, 0, 1) and (0, 1, 1). The total volume is eight cubes.
The front view looks along y. The occupied (x, z) cells are (0, 0), (1, 0), (2, 0) and (0, 1), giving an L silhouette three units wide and two units high. The right view looks along x. The occupied (y, z) cells are (0, 0), (1, 0), (0, 1) and (1, 1), giving a two by two rectangle. The top view looks along z. All six base cells appear, giving a three by two rectangle.
Check the shared extents: front and top both span x from 0 to 2; front and right both span z from 0 to 1; right and top both span y from 0 to 1. These agreements are necessary but not sufficient for a correct drawing, so also confirm that each silhouette was built from the cell list rather than copied from a neighbouring view.
A common failure is mixing axes between views, especially using x as the horizontal coordinate in the right view. Another is drawing a rectangle where the cell list gives an L shape because a column was overlooked. A third is treating an occupancy mask as a complete line drawing and adding internal seams that the model does not define.
Use a short written audit after drawing: list the distinct coordinate pairs for each view, count them, and compare with the drawn filled cells. If the counts differ, the drawing and the cell list disagree. Keep the audit on the page so a reader can follow the reasoning without needing a separate answer key.
Orthographic exercises have multiple valid presentation choices, such as line weight and label placement, so judge the reasoning and consistency rather than a single exact picture. The occupancy method is a teaching aid for relating a defined model to three views. It is not a clinical anatomy method and not a substitute for engineering or construction documentation.
A model has eight unit cubes: six at z = 0 covering x = 0, 1, 2 and y = 0, 1, plus cubes at (0, 0, 1) and (0, 1, 1). Find the front, right and top occupancy silhouettes and check shared extents.
Front view along y: distinct (x, z) pairs are (0, 0), (1, 0), (2, 0) and (0, 1), an L shape three wide and two high. Right view along x: distinct (y, z) pairs are (0, 0), (1, 0), (0, 1) and (1, 1), a two by two rectangle. Top view along z: distinct (x, y) pairs cover all six base cells, a three by two rectangle. Front and top agree on x from 0 to 2; front and right agree on z from 0 to 1; right and top agree on y from 0 to 1. The total volume is eight cubes. These checks cover occupancy and dimensions only, not hidden internal seams.
It shows which grid cells contain at least one cube along the viewing direction. It does not by itself establish which internal edges would be visible or hidden in a finished line drawing.
Shared axes must agree. Front and top share the x extent, front and right share the z extent, and right and top share the y extent. A mismatch signals an axis or cell-list error.
No. It is a teaching exercise about projection and view correspondence. Do not use it as a fabrication or construction document.
