"use strict";

function round2(x) { return Math.round(x * 100) / 100; }

module.exports = {
  slug: "sphere-and-cylinder-volumes",
  title: "Sphere and cylinder volume and surface area",
  deck_category: "geometry",
  description: "Computes the volume and total surface area of a sphere or a right circular cylinder.",
  inputs: [
    { name: "shape", type: "string", required: true, description: "Which solid to measure.", enum: ["sphere", "cylinder"] },
    { name: "radius", type: "number", unit: "length units", required: true, description: "Radius of the sphere or cylinder.", min: 0 },
    { name: "height", type: "number", unit: "length units", required: false, description: "Height of the cylinder (ignored for sphere).", min: 0 }
  ],
  outputs: [
    { name: "volume", unit: "cubic length units", description: "Volume of the solid." },
    { name: "surface_area", unit: "square length units", description: "Total surface area of the solid." }
  ],
  steps: [
    "For a sphere of radius r: volume = (4/3) * pi * r^3; surface area = 4 * pi * r^2.",
    "For a right circular cylinder of radius r and height h: volume = pi * r^2 * h; total surface area = 2*pi*r*h + 2*pi*r^2 (the side plus both circular ends).",
    "Round both results to 2 decimals."
  ],
  constants: [
    { name: "pi", value: 3.14159265358979, unit: "dimensionless", source: 0 }
  ],
  sources: [
    { kind: "edition_page", value: "Standard geometry reference (e.g. Coxeter, H.S.M. Introduction to Geometry, 2nd ed., Wiley, 1969).", title: "Sphere and cylinder volume and surface area formulas", publisher: "Wiley", retrieved_utc: "2026-09-30T19:49:00Z", note: "Standard solid-geometry formulas." }
  ],
  disclaimer: null,
  questionText(inputs) {
    if (inputs.shape === "sphere") return `What are the volume and surface area of a sphere with radius ${inputs.radius}?`;
    return `What are the volume and surface area of a cylinder with radius ${inputs.radius} and height ${inputs.height}?`;
  },
  run(inputs) {
    const { shape, radius, height } = inputs || {};
    if (shape !== "sphere" && shape !== "cylinder") throw new Error("shape must be sphere or cylinder");
    if (typeof radius !== "number" || radius <= 0) throw new Error("radius must be a positive number");
    let volume, surface;
    if (shape === "sphere") {
      volume = (4 / 3) * Math.PI * radius ** 3;
      surface = 4 * Math.PI * radius ** 2;
    } else {
      if (typeof height !== "number" || height <= 0) throw new Error("height must be a positive number for a cylinder");
      volume = Math.PI * radius ** 2 * height;
      surface = 2 * Math.PI * radius * height + 2 * Math.PI * radius ** 2;
    }
    volume = round2(volume);
    surface = round2(surface);
    return { answer: `volume ${volume.toFixed(2)}, surface area ${surface.toFixed(2)}`, values: { volume, surface_area: surface } };
  },
  examples: [
    {
      name: "worked example",
      inputs: { shape: "sphere", radius: 3 },
      expected: { answer: "volume 113.10, surface area 113.10" },
      check: "By hand: volume=(4/3)*3.14159265*27=113.0973 rounds to 113.10; surface=4*3.14159265*9=113.0973 rounds to 113.10. It is an independently known fact that a sphere's volume and surface area are numerically equal precisely at radius 3, since (4/3)pi*r^3=4*pi*r^2 solves to r=3, giving a built-in cross-check that both values should match."
    },
    {
      name: "test vector: cylinder",
      inputs: { shape: "cylinder", radius: 2, height: 5 },
      expected: { answer: "volume 62.83, surface area 87.96" },
      check: "By hand: volume=3.14159265*4*5=62.8319 rounds to 62.83; surface=2*3.14159265*2*5+2*3.14159265*4=62.8319+25.1327=87.9646 rounds to 87.96."
    }
  ]
};