Source: https://guthlabs.ai/docs/instruments/3d-solid-volume-surface-area-calculator/

instrument / verified-clean

# 3D Solid Volume/Surface Area Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/3d-solid-volume-surface-area-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/3d-solid-volume-surface-area-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/3d-solid-volume-surface-area-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/3d-solid-volume-surface-area-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)

**Tranche**: tranche-4

**Evidence ID**: t4-177

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The explicitly supplied sphere and cone volume formulas are standard and correct under the stated assumptions, but the catalog claim is broader than the formulas provided. The exact ambiguity requiring review is whether 'surface area' means total closed surface area, lateral area, or exposed area, and which dimensions define prism, pyramid, frustum, and torus inputs.

### Formula and scope findings

- The sphere volume formula V=(4/3)πr³ is correct when r is the radius.

- The cone volume formula V=(1/3)πr²h is correct for a right circular cone when r is base radius and h is perpendicular height.

- SA formulas are unspecified: the specification does not define whether surface area means total, closed, lateral, or exposed area.

- Formulas are missing for prism, pyramid, cylinder, frustum, and torus despite those solids being claimed outputs.

- Prism and pyramid calculations require base shape and dimensions; 'dimensions' alone is ambiguous.

- A torus requires major radius R and minor-tube radius r, plus a constraint such as R>r for a standard ring torus.

### Unit assumptions

- All dimensions in each calculation must use the same length unit.

- Volume outputs use cubic length units and surface-area outputs use square length units.

- r means radius, not diameter; h means perpendicular height.

- π is assumed to be the mathematical constant, evaluated here as 3.141592653589793.

- Test vectors for cone and frustum use total closed surface area, including the base or bases.

- The frustum test uses the standard right-circular-frustum formulas V=(πh/3)(R²+Rr+r²) and SA=π(R²+r²+(R+r)s), where s=sqrt((R-r)²+h²).

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not state torus validity regimes or spindle-torus handling, so inputs with R<r can produce a plausible but geometrically inappropriate result. Extreme sphere radii also overflow the volume in ordinary JavaScript Number arithmetic, and negative cone heights expose an unstated sign convention.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "solid_type": "sphere",
    "radius": 3,
    "length_unit": "m"
  },
  "expected_outputs": {
    "volume": 113.09733552923255,
    "volume_unit": "m^3",
    "surface_area": 113.09733552923255,
    "surface_area_unit": "m^2"
  },
  "working": "V=(4/3)πr³=(4/3)π(3³)=(4/3)π(27)=36π=113.09733552923255 m^3. SA=4πr²=4π(3²)=36π=113.09733552923255 m^2."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`