Cross sections
Imagine slicing a box, prism or pyramid. Choose the shape of the cut.
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Turn the example to see where the clear sheet cuts the solid. In each question, picture the hidden part of the cut before choosing its shape.
Prisms, pyramids and off-center cuts
6 questions · No time limit
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Example
Example
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- Questions answered
- 0 / 6
- Active time
- 0:00
What shape does the slice make?
Turn the example to see where the clear sheet cuts the solid. In each question, picture the hidden part of the cut before choosing its shape.
Start to get a new set.
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Follow where the plane meets the solid. Compare the shapes of the choices. Selecting an option submits your answer.
After answering, the actual section is highlighted inside the solid and shown face-on beside it. Turn view changes only the viewing direction. Choose Next question when ready.
A plane cuts the solid into a flat polygon. Choices can have the same number of sides: use their proportions and angles to tell them apart.
Finish all six questions to save a result on this browser. Leaving early saves no completed round. Active time counts only while this page is in the foreground; there is no time limit or speed bonus.
Use Tab and Enter or Space to select a shape. Keys 1–5 select an available choice, except when another control is focused. The figures require sight.
About this practice
Each question shows a cube or a rectangular block with a see-through sheet through it. The sheet is the cutting plane. Lines on the faces you can see mark the cut, and the rest is hidden. You choose the flat shape the cut leaves from four outlines, with three, four, five and six sides.
What it measures, and what it does not
It asks you to picture the inside of a solid from the outside: where a flat cut enters and leaves each face. It uses only boxes, so round solids such as cones and cylinders are not part of it. Six questions make a short sample.
What each level changes
- Easy: three straight slices with four sides and three corner cuts with three.
- Standard: three four-sided cuts, one corner cut and two cuts with five sides.
- Challenge: one four-sided cut, two with five sides and three with six.
Every round has one cube and five boxes of other proportions.
A worked example
The four choices
- Count the cut lines on the faces you can see: three.
- Follow the sheet around the back. It crosses two more faces you cannot see.
- Each crossed face gives the cut one side, so the cut has five sides: a pentagon. That is option B.
What your result means
You get one point for each correct shape, out of six. Speed does not affect the score, and there is no time limit. After each answer the practice shades the whole cut, draws it flat beside the solid, and lets you turn the view, so you can find where each side came from.
For four more worked examples and the common confusions, read the guide Cross section test: how to find the shape of a cut. For the method, try the lesson Cut a solid.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used