technique shows how to approximate the volume of any convex body using a membership oracle. Units The general form of a unit of volume is the cube (x3) of a unit of length. For instance, if the metre (m) is chosen as a unit of length, the corresponding unit of volume is the cubic metre (m3). Thus, volume is a SI derived unit and its unit dimension is L3. The metric units of volume uses metric prefixes, strictly in powers of ten. When applying prefixes to units of volume, which are expressed in units of length cubed, the cube operators are applied to the unit of length including the prefix. An example of converting cubic centimetre to cubic metre is: 2.3 cm3 = 2.3 (cm)3 = 2.3 (0.01 m)3 = 0.0000023 m3 (five zeros). Commonly used prefixes for cubed length units are the cubic millimetre (mm3), cubic centimetre (cm3), cubic decimetre (dm3), cubic metre (m3) and the cubic kilometre (km3). The conversion between the prefix units are as follows: 1000 mm3 = 1 cm3, 1000 cm3 = 1 dm3, and 1000 dm3 = 1 m3. The metric system also includes the litre (L) as a unit of volume, where 1 L = 1 dm3 = 1000 cm3 = 0.001 m3. For the litre unit, the commonly used prefixes are the millilitre (mL), centilitre (cL), and the litre (L), with 1000 mL = 1 L, 10 mL = 1 cL, 10 cL = 1 dL, and 10 dL = 1 L. Litres are most commonly used for items (such as fluids and solids that can be poured) which are measured by the capacity or size of their container, whereas cubic metres (and derived units) are most commonly used for items measured either by their dimensions or their displacements. Various other imperial or U.S. customary units of volume are also in use, including: cubic inch, cubic foot, cubic yard, acre-foot, cubic mile; minim, drachm, fluid ounce, pint; teaspoon, tablespoon; gill, quart, gallon, barrel; cord, peck, bushel, hogshead. The smallest volume known to be occupied by matter is probably the proton, with its radius is known to be smaller than 1 femtometre. This means its volume must be smaller than , though the exact value is still under debate as of 2019 as the proton radius puzzle. The van der Waals volume of a hydrogen atom is far larger, which ranges from to