Spin a shape
Picture the solid a flat shape sweeps out as it spins round a line, and pick it from four.
Example
Example
Example · Standard
Which solid does the shape sweep out as it spins once round the dashed line?
Read the drawing as text
Corners of the shape, as (units left of the dashed line, units up from the bottom): (3, 0), (2, 0), (1, 2), (1, 3), (3, 3).
Half a turn later the shape is on the other side of the line, drawn dashed. Together the two halves are the solid cut in half along the line. The far side of the shape is 3 units from the line, so the solid is 6 units across. The shape never reaches the line, so the gap makes a hole all the way through, at least 2 units across. The solid is 3 units high, as high as the shape.
Steps and slants, some a unit away from the line so the solid has a hole
6 questions · No time limit
- Questions answered
- 0 / 6
- Active time
- 0:00
Ready to start?
Each grid square is 1 unit. The shape spins once, all the way round the dashed line, and every point of it stays the same distance from the line. Pick the solid it sweeps out. At Challenge some questions go the other way: pick the shape that sweeps out the solid shown.
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Reload pageOn 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 usedHelp
Every point of the shape travels in a circle round the dashed line. A point 2 units from the line makes a circle 4 units across, so the part of the shape furthest from the line sets how wide the solid is, and the solid is as high as the shape. Where the shape does not reach the line, the gap becomes a hole. When the line runs through the shape, both sides spin, and at each height the side that reaches further sets the width. Every wrong option is a real solid of revolution, from the same shape spun about another line or from another shape, so each question has exactly one right answer.
Each round has six questions and no time limit. Choosing an answer locks it. Review the steps, then move to the next question. Finish all six to save the round. Active time includes reviewing the steps, but does not count time when this page is hidden. Speed does not affect your score.
Use Tab and Enter or Space to choose an answer. The number keys also select answers, except when another control is focused. After an answer, Enter goes to the next question.
Original practice puzzles, not a standardized assessment.
About this practice
Practice picturing turned solids: a flat shape spins once round a dashed line, and you pick the solid it sweeps out.
Report a problem
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