Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full behavioral burden, and it discloses almost nothing: no determinism/purity statement, no unit assumptions, no indication of what form the result takes. It also hides that height and radius are supplied as strings rather than numbers, which affects invocation.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Two short clauses, front-loaded with the resource and quantity, with zero padding. Its brevity is efficient even if it leaves gaps elsewhere.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a two-parameter math utility with fully described parameters and no output schema, the essential inputs are covered. It still omits what the tool returns (a scalar? an object?) and the total-vs-lateral distinction, which is the main gap for correct selection.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the two parameters are already documented as 'Height to process' and 'Radius to process'. The description adds no further meaning (e.g. units or positivity constraints), so the baseline 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description names a specific computed quantity ('Surface area') and resource ('cylinder'), so an agent knows this is a cylinder surface-area calculator. It does not, however, distinguish itself from the sibling x402-cylinder-lateral-surface, leaving the total-vs-lateral ambiguity to be inferred.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

There is no when-to-use guidance, no prerequisites (e.g. positive radius), and no routing to alternatives such as x402-cylinder-lateral-surface or x402-cylinder-volume. The agent must infer selection purely from the tool name.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.