solid-volume-by-decomposition
The volume of a three-dimensional region is found by expressing it as a sum, difference, or fixed fraction of primitive solids — prisms, cylinders, spheres, pyramids, cones, or tetrahedra — whose dimensions are read off the configuration. The 3D analog of compound-area decomposition: the work is choosing the split, not any single volume formula. Often a total volume is given and a length is back-solved.
How to solve
- Swap the bounding primitive from a box to a cylinder — the wedge / fraction argument is structurally identical
- Give the total volume and ask for a missing length (back-solve) instead of asking for the volume directly
- Change decomposition_mode from fraction-of-whole to sum-of-primitives (e.g. a capsule = cylinder + two hemispheres)
Sub-archetype mix (2)
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- solid-sum-of-primitives 38% (11)
The target region is the union of disjoint primitive solids (e.g. a central cylinder capped by two hemispheres, or a stack of prisms); add the primitive volumes, often back-solving a length from a stated total volume.
- solid-fraction-or-difference 62% (18)
The target sub-solid is a fixed fraction of, or a primitive subtracted from, a bounding solid (a wedge that is half a cylinder, a pyramid or corner tetrahedra carved from a box); compute it as that fraction or difference of simpler volumes.
no figureamc10-2003A-3no figureamc10-2003B-17no figureamc10-2010A-17no figureamc10-2011A-24no figureamc10-2012B-23
amc10-2018B-10
amc10-2025B-19no figureamc12-2003A-3no figureamc12-2003B-13
amc12-2005A-17no figureamc12-2007A-20no figureamc12-2008A-18no figureamc12-2008B-11no figureamc12-2008B-18no figureamc12-2010A-9no figureamc12-2016B-23 amc12-2025B-15
amc8-2008-21
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 5 1
- Gr 6 1
- Gr 7 3
- Gr 8 9