Cube views
Read cube views, find a missing view, or choose a clue that distinguishes two stacks.
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Example
Example
Example
Top view first, then front, right and back views. Five choices per question.
3 × 3 grid · Up to 3 cubes high · 4 questions
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No time limit
- Shapes answered
- 0 / 4
- Active time
- 0:00
Which grid matches this view?
A figure made of stacked cubes appears. Choose the flat grid you would see looking straight down from above or straight at it from the front, as the question asks.
Right view: front on the left, back on the right.
Read the right view
The top view shows where stacks stand. The front view gives the tallest stack in each column from left to right. In the right view, read from front to back and use the tallest stack in each row of the top view.
- Correct answers
- Active time
The top view shows the footprint: each stack is one square. In the front view, overlapping stacks share a column, which reaches the tallest height along that line of sight.
Review answers
Explore the method
Separate a stack’s footprint from its height seen from the front.
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How this data is usedHelp
In “Read a solid,” choose the top, front, right or back view of the cube stack shown.
Look straight down for the top view. Each stack occupies one square, whatever its height. The nearest corner of the figure is the grid’s bottom right; the farthest is its top left.
For the front view, look straight at the figure. At each horizontal position, stacks behind one another overlap: use the greatest height along that viewing depth. The bottom row is the ground, with no gaps or floating squares.
In the current Read a solid practice, levels 1–2 ask for top views. Front views join at level 3, right views at level 5, and back views at level 7.
All cubes are stacked from the ground with no gaps. Use both given views together. On the top grid, Back is at the top and Front is at the bottom. On the upright right view, Front is on the left and Back is on the right. Each right-view column reaches the tallest stack in that row of the top grid.
In “Choose the extra clue,” two different cube stacks have the same two given views. Choose the only observation that gives different results for A and B: the unused view, the total number of cubes, or the height of a specified column.
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About this practice
Read a solid from four directions, find a missing right view, or choose the extra clue that distinguishes two stacks.
A view is a flat outline of a solid from one direction. Read a solid starts with a cube stack; Find the missing view starts with top and front grids. Choose the extra clue asks what measurement would tell two possible solids apart. All three modes leave the question visible and have no time limit.
Read a solid: overlap the stacks
From above, mark one square for every occupied position, whatever its height. From the front, stacks behind one another overlap. Take the greatest height at each position across the figure, without adding the heights together.
Level 3. Find the front view. The matching front view. The ground is at the bottom.
- The left position contains stacks 4, 3, 2 cubes high, from back to front. Their front outline is 4 squares high.
- The middle position reaches 2 squares; the right reaches 1. The front view therefore has heights 4, 2, 1, left to right.
- Keep the viewing direction fixed. From the right, the front of the figure appears on the grid’s left. From the back, left and right reverse compared with the front view.
Find the missing view: use both grids
The top grid tells you where stacks stand. The front grid limits their heights. A filled top square does not mean a stack is only one cube high, and the front height need not belong to every stack behind it.
Top
Back
Front
Front
Ground at the bottom
- The front heights are 1, 2, 2, left to right. The top grid’s middle column has a stack only in the front row, so that stack must be 2 cubes high. Its right column has a stack only in the back row, so that stack must be 2 high.
- The middle row holds only a stack in the left column, whose height is 1. The right view is therefore 2, 1, 2 from front to back: option 1.
Choose the extra clue: look for a difference
Two different solids can have the same views. Compare what each proposed clue tells you about solid A and solid B. A clue distinguishes them only if its value differs.
Rows run from front to back; columns run from left to right in the front view.
Given views, shared by A and B
The top and right views match. Which extra clue would tell these solids apart? Row 1 is nearest the front; columns run left to right on the numbered base.
| Clue | Solid A | Solid B |
|---|---|---|
| 1. Column height: row 2, column 2 | 1 | 1 |
| 2. Column height: row 1, column 2 | 2 | 1 |
| 3. Total cubes | 13 | 13 |
| 4. Column height: row 2, column 1 | 2 | 2 |
| 5. Front view | 2, 2, 2 | 2, 2, 2 |
- Both solids contain 13 cubes. Their front views also match: each position reaches 2 cubes high. Neither clue separates A from B.
- At row 1, column 2, A has a height of 2 and B has a height of 1. That difference makes option 2 the answer. The other two named columns have the same height in both solids.
- A different height can be hidden behind a taller stack in a flat view. Check the named position instead of assuming matching outlines mean identical solids.
What the levels and results mean
In the current Read a solid practice, levels 1–2 use top views; levels 3–4 add front views; levels 5–6 add right views; levels 7–8 add back views. Figures grow from a 3 × 3 base with heights up to 2 cubes at level 1 to a 5 × 5 base with heights up to 6 at level 8. Each question has five choices.
Find the missing view uses four choices. Levels 1–2 use a 2 × 2 base and heights up to 2; levels 3–4 widen the base to 3 × 3; levels 5–8 allow heights up to 3. The two given views determine one right view, even when some individual stack heights remain uncertain.
Choose the extra clue offers five choices: the unused view, the total cube count and three named column heights. Exactly one choice distinguishes the two solids. Levels 1–4 use a 3 × 3 base; levels 5–8 use 4 × 4. Maximum heights rise from 2 at levels 1–2, to 3 at levels 3–6, and 4 at levels 7–8.
A completed round scores correct choices out of 3 to 7, depending on level. Speed does not affect that count. Compare rounds within the same mode and level, and use the answer review to distinguish a height mistake from a reversed view. Ending early does not save a completed round.
The lesson for this mode: Read top and front views. The research guide Spatial reasoning tests: the six question types explains where view questions fit among other spatial tasks, and Cross section test: how to find the shape a cut leaves covers a related task.
For a broader mix of practices, explore the spatial practice test. Sign in free to start a test.
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On by default unless you turn it off. Saved choices are kept. Shares starts, completions, replays and error categories. For ChatGPT visits, starts and completions may include the first QuickenBrain page and country. No answers, drawings or names.
How this data is used