How much does this shape hold?

How it works

Volume is how much space a solid fills, counted in cubes of the length unit: a box 4 m long, 3 m wide and 2 m high holds 4 × 3 × 2 = 24 cubes of 1 m × 1 m × 1 m, so 24 m³. A cubic metre is 1 000 litres, so that box holds 24 000 litres of water. The surface area is the total area of its faces, what you would paint or wrap.

Solids with a constant cross-section, such as a box or a cylinder, are the base area times the height: a cylinder is π × r² × h. Pointed solids hold a third of that: a cone is π × r² × h / 3 and a pyramid l × w × h / 3. A sphere is 4/3 × π × r³; a sphere 1 m across (r = 0.5 m) holds about 0.52 m³, or 524 litres. Source: CRC Standard Mathematical Tables and Formulae.

Every volume here is exact for the ideal shape. The ellipsoid's surface has no simple formula and uses Knud Thomsen's approximation, within about 1 %. Real containers have walls, sloping floors and rounded corners, so measure the inside and use an average depth.