Pick a solid, type its dimensions and watch it rebuild in 3D. Get the volume, total and lateral surface area, capacity in litres and gallons, diagonals and slant heights — with the formula and working shown. Cube, cuboid, sphere, hemisphere, cylinder, cone, frustum, square pyramid, triangular prism, hexagonal prism, torus and ellipsoid.
Prisms and cylinders all share V = base area × height. Pyramids and cones are exactly a third of that: V = ⅓ × base × h. A sphere is V = 4⁄3 πr³, A = 4πr² — Archimedes showed it fills two-thirds of its bounding cylinder, volume and area alike.
Frustum (a cone with the top cut off): V = ⅓πh(R² + Rr + r²), slant s = √(h² + (R−r)²), lateral area π(R + r)s. Torus: V = 2π²Rr², A = 4π²Rr (Pappus's theorems). Ellipsoid area has no closed form; we use Knud Thomsen's approximation (error < 1.1%).
Capacity: 1 litre = 1000 cm³ = 0.001 m³. 1 US gallon = 3.785 L, 1 imperial gallon = 4.546 L.
Worked example: a cylinder with r = 5 cm, h = 10 cm has V = π × 25 × 10 ≈ 785.398 cm³ (0.785 L) and total area 2π × 5 × (5 + 10) ≈ 471.239 cm².