# x402.forgemesh.io Solid Geometry Calculator

> x402.forgemesh.io Solid Geometry Calculator is a paid API for AI agents from x402.forgemesh.io, paid per call via x402, $0.002/call, status unknown (last checked 2026-09-16).

Calculates exact volume and surface area for spheres, cylinders, cones, cubes, and rectangular prisms given structured dimension inputs

## Facts

- Endpoint: POST https://x402.forgemesh.io/volume-calculator
- Price: $0.002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-16
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/x402-forgemesh-io-solid-geometry-calculator-e67ce96b
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_zYsA7RE_POn_xdxblVEIK

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability x402-forgemesh-io-solid-geometry-calculator-e67ce96b -d '<json body>'
```

Example prompt: Can you calculate the exact volume and surface area of a cylinder with a radius of 4 meters and a height of 10 meters?

## When to prefer this

Use this endpoint when you need a precise, checked numerical result for solid geometry — volume and surface area — for one of the supported standard shapes (sphere, cylinder, cone, cube, rectangular prism). Ideal for packaging design, container sizing, construction estimation, or STEM education tools where accuracy matters more than mental approximation.

## Known failure modes

- Missing required dimensions for the specified shape (e.g., radius not provided for sphere)
- Invalid shape type string not matching accepted enum values
- Non-numeric string values passed for dimension fields
- Payment failure or insufficient USDC balance ($0.002 per call)

## How this service works

Solid geometry calculator returning exact volume and surface area for spheres, cylinders, cones, cubes, and rectangular prisms from structured dimension inputs. Built for packaging design, tank and container sizing, construction estimates, and STEM education tools that need a checked number rather than a mental estimate.

## Output

Returns the exact volume and surface area for the specified 3D shape, computed from the provided dimension inputs such as radius, height, length, width, or side length.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "a": {
   "type": "string"
  },
  "b": {
   "type": "string"
  },
  "c": {
   "type": "string"
  },
  "base": {
   "type": "string"
  },
  "side": {
   "type": "string"
  },
  "shape": {
   "type": "string",
   "description": "circle|rectangle|triangle|sphere|cylinder|cone|cube|rectangular_prism"
  },
  "width": {
   "type": "string"
  },
  "height": {
   "type": "string"
  },
  "length": {
   "type": "string"
  },
  "radius": {
   "type": "string"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "shape": "sphere",
  "volume": 523.598776,
  "surface_area": 314.159265
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/x402-forgemesh-io-solid-geometry-calculator-e67ce96b/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from x402.forgemesh.io](https://www.zero.xyz/host/x402.forgemesh.io/llms.txt)