Verified calculation capability

Solid geometry Calculation Capability

Right circular sphere, cylinder, cone, ring torus, and conical frustum. Discovery /sphere, /cylinder, /cone, /frustum. Not the circle-only page, not a vector, not ISO 5167-5, not prism/pyramid, not CAS. · Math · Geometry

Capability ID math.geometry.solid · version 1.1.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Sphere

Sphere: V = (4/3)πr³, A = 4πr²
Cylinder: V = πr²h, A = 2πr(r+h)
Cone: V = (1/3)πr²h, l = √(r²+h²)
Frustum: V = (1/3)πh(R² + Rr + r²)

Solve modes: sphere · cylinder · cone · torus · frustum

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`r`	—	—	input / output
`h`	hydrogen-ion concentration	—	input / output
`R`	—	—	input / output
`volume`	—	—	output
`surface`	—	—	output
`lateral`	—	—	output
`slant`	—	—	output
`cylinder`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Euclidean 3-space
Right circular solids
Ring torus R > r
Not the circle-only page
Not a vector
Not ISO 5167-5
Not prism / pyramid
Not CAS

Example

One numerical check. The calculator page holds worked steps and FAQ.

sphere r=1 → V=4π/3

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.1.0
Evidence tests: 16/16 calculation tests · golden 5/5 · boundary 3/3 · property 8/8
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.1.0 (workspace artifacts agree)

Production attestation: Embedded snapshot: unpublished · Build schema 1.1.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T21:41:55.460Z
Last production check: 2026-09-18T21:41:55.460Z
Public / cache: —
Origin: —

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 3/3.

Tool id: solid-geometry
Engine: solid-geometry
REST: POST /api/v1/calc/solid-geometry
MCP: execute_calculation with capability_id: "math.geometry.solid"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.1.0)
Versioned output schema: Immutable pin (1.1.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

ISO 80000-2:2019 Quantities and units — Mathematics

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.geometry.solid"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.1.0) when reproducibility matters. Full protocol notes: MCP docs.