task_geometry__solid_revolution__revolution_double_cone_volume_value

Contract

1. Domain: geometry
2. Scene id: solid_revolution
3. Task id: task_geometry__solid_revolution__revolution_double_cone_volume_value
4. Supported query_id values: single
5. Answer schema: number
6. Answer precision: one_decimal
7. Annotation schema: bbox_map
8. Scalar annotation checked: true (not scalar-eligible; the task binds source and result shape witnesses)

Program Contract

• solve_formula(visible_solid_revolution_measurements, formula_schema=double_cone_volume_from_triangle, target=volume); scene=solid_revolution; scope=revolution_double_cone_volume_value

Reasoning Operations

Families: transformation, formula_evaluation

Query IDs

• single: an isosceles triangle is rotated 360 degrees around its marked base axis; solve the resulting double-cone volume from the visible radius and half-height.

Prompt Bundle

• Prompt text is loaded from src/trace_tasks/resources/prompts/geometry/solid_revolution/geometry_solid_revolution_v1.json.
• Prompt modes: answer_only and answer_and_annotation.

Annotation

The annotation is a bbox_map with role-bound pixel boxes for the source generating diagram and the resulting solid. Numeric labels, individual dimension marks, the rotation arrow, and formula cues remain visible scene content plus private verifier metadata, not separate annotation targets:

• source_diagram_bbox
• resulting_solid_bbox

Determinism

Generation is deterministic for a fixed seed, params, config, and prompt bundle version.

Source

• Config: src/trace_tasks/resources/configs/domains/geometry/solid_revolution.yaml
• Prompt bundle: src/trace_tasks/resources/prompts/geometry/solid_revolution/geometry_solid_revolution_v1.json
• Task module: src/trace_tasks/tasks/geometry/solid_revolution/revolution_double_cone_volume_value.py