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 43% (6)
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 57% (8)
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.
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