{
  "schemaVersion": 1,
  "slug": "cone-volume-calculator",
  "category": "geometry",
  "kind": "implementation",
  "independentValidation": false,
  "implementationHash": "71bb9b3effc22a6f19273b811f64b32032353e67fa49ef279a4a345d17bc90d9",
  "provenance": "Generated from the calculation contract used by the published page. Publication is not external validation.",
  "sourceFiles": [
    "data/calculators/cone-volume-calculator.json",
    "src/engine.js"
  ],
  "runtimeSource": "/sources/engine.txt",
  "runtimeHash": "5c888d8898afbdee36267bb9977829e1e2ac568f6677c8ee87469c139864645c",
  "scope": "The compute function records implemented equations, constants, lookup tables and custom rules. Inputs record defaults and allowed values; outputs record precision and units. Defaults are examples, not recommendations. General background references are not evidence for this specific algorithm.",
  "publishedFormula": {
    "formula": "V = π × r² × h ÷ 3; l = √(r² + h²); A_l = π × r × l",
    "vars": [
      [
        "r",
        "base radius"
      ],
      [
        "h",
        "height"
      ],
      [
        "l",
        "slant height"
      ],
      [
        "V",
        "volume"
      ],
      [
        "A_l",
        "lateral area"
      ]
    ],
    "note": "Total surface area = lateral area + πr² (base area)."
  },
  "externalEvidence": {
    "reviewedAt": "2026-10-04",
    "sources": [
      {
        "name": "OpenStax — Geometric formulas",
        "url": "https://openstax.org/books/prealgebra/pages/c-geometric-formulas"
      }
    ],
    "basis": "V = πr²h/3; slant height = sqrt(r² + h²).",
    "limitations": "Ideal Euclidean shapes; use consistent length units. A diameter is twice the radius.",
    "implementationHash": "71bb9b3effc22a6f19273b811f64b32032353e67fa49ef279a4a345d17bc90d9",
    "domain": "math"
  },
  "contract": {
    "compute": "const PI = Math.PI;\nconst slant = Math.sqrt(radius*radius + height*height);\nconst base = PI*radius*radius;\nconst lateral = PI*radius*slant;\nreturn { volume: base*height/3, lateralArea: lateral, totalArea: lateral+base, baseArea: base, slantHeight: slant };",
    "inputs": [
      {
        "name": "radius",
        "type": "number",
        "default": 5,
        "min": 0.01,
        "max": 100000,
        "step": 0.01
      },
      {
        "name": "height",
        "type": "number",
        "default": 12,
        "min": 0.01,
        "max": 100000,
        "step": 0.01
      }
    ],
    "outputs": [
      {
        "name": "volume",
        "precision": 3,
        "unit": "unit³"
      },
      {
        "name": "lateralArea",
        "precision": 3,
        "unit": "unit²"
      },
      {
        "name": "totalArea",
        "precision": 3,
        "unit": "unit²"
      },
      {
        "name": "baseArea",
        "precision": 3,
        "unit": "unit²"
      },
      {
        "name": "slantHeight",
        "precision": 4,
        "unit": "unit"
      }
    ],
    "interpret": null
  }
}