Translations of Encyclopedia about Mathematics

Surface Measurements

The basic unit of measuring surfaces is the square meter (m²). Using prefixes, we find the most common forms of measuring surfaces to be the square millimetre (mm²), the square centimetre (cm²),the square decimetre (dm²) and the square kilometre (km²). The are (a) and the hectare (ha) are used for measuring larger surface areas. Calculating the surface area of different shapes will be explained in the geometry section.

The square metre is a surface area 1 metre wide and 1 metre long, referred to as a square. All other units are defined in the same manner. For example, a square metre is a surface area which is 1 dm wide and 1 dm long, calculated as

1 dm . 1 dm = 1 dm²
1 dm

1 dm

In the metric decimal system, the individual units of measuring surfaces are also precisely defined by a ratio to the metre, simplifying conversions between the various units:

1 m² = 0.000001 km²	1 km² = 1 000 000 m²
1 m² = 0.0001 ha	1 ha = 10 000 m²
1 m²= 0.01 a	1 a = 100 m²
1 m² = 100 dm²	1 dm² = 0.01 m²
1 m² = 10 000 cm²	1 cm² = 0.0001 m²
1 m² = 1 000 000 mm²	1 mm² = 0.000001 m²

As with length measurements, here also there are other systems of defining surface areas, such as circular mils (cmil) when calculating the surface area of circles, square inches – in², square chains – ch², square yards yd², square feet – ft², square miles –mi², and the acre – ac.

Surface measurements can be converted between the various systems used using a system of multiplication and division, a few samples of which are shown below:

circular mils (cmil) . 506.7	m m²
m m² . 0.002	circular mils (cmil)
square inches in² . 645.2	mm²
mm² . 0.0015	square inches (in²)
square inches in² . 6,452	cm²
cm² . 0.15	square inches (in²)
square chains ch² . 404.686	m²
m² . 0.0025	square chains (ch²)
square yards yd² . 0.836	m²
m² . 1.196	square yards (yd²)
square foot ft² . 0.093	m²
m² . 10.764	square foot (ft²)
square mils mi² . 2.59	km²
km² . 0.386	square mils (mi²)
square mils mi² . 258.999	ha
ha . 0.0039	square mils (mi²)
acre ac . 0.405	ha
ha . 2.471	acre (ac)

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Volume and Hollow Measurements

The basic unit of measurement of volume is the cubic metre (m³). With the use of prefixes, once again, we obtain the other commonly used units of measuring volume: the cubic millimetre (mm³), cubic centimetre (cm³), cubic decimetre (dm³) and the cubic kilometre (km³). Calculation of the volume of different objects will be covered in the geometry section.

One cubic metre is a volume of 1 metre height, 1 metre width and 1 metre length, or a cube with sides 1 metre long.

All other units are defined in the same manner, such that, for example, a cubic centimetre is a volume of 1 cm height, 1 cm width and 1 cm length, calculable in the following manner:

1 cm . 1 cm . 1 cm = 1 cm³

In the metric decimal system, the different units relate in ratio to the metre, simplifying conversion between the various units:

1 m³ = 0.000000001 km³	1 km³ = 1000000000 m³
1 m³ = 1000 dm³	1 dm³ = 0.001 m³
1 m³ = 1000000 cm³	1 cm³ = 0.000001 m³
1 m³ = 1000000000 mm³	1 mm³ = 0.000000001 m³

If we measure the volume of some liquid, we are referring to a hollow space and use the litre (l) as a unit of measurement. With the use of prefixes, we then obtain the other, commonly used units of measurement: the millilitre (ml), centilitre (cl), decilitre (dl), decalitre (dal) and the hectolitre (hl).

One litre (of water at sea level) is equal to one cubic decimetre.

Therefore: 1 l = 1 dm³ = 1000 cm³

We often use these calculations when describing the qualities of a particular automobile. For example, we might say that a cylinder’s volume is 1.6 litres, although in technical practice we would write 1,600 cm³. Hollow spaces can also be converted to volume spaces.

In the metric decimal system, all hollow space measurements relate to a precise ratio with the metre, simplifying conversion between the various units:

1 l = 0.01 hl 1 hl = 100 l
1 l = 0.1 dal 1 dal = 10 l
1 l = 10 dl 1 dl = 0.1 l
1 l = 100 cl 1 cl = 0.01 l
1 l = 1000 ml 1 ml = 0.001 l

As with the other forms of measurement, there also exist other methods of measuring volume, such as cubic inches (in³), fluid ounces (fl oz), quarts (qt), gallons (gal), pints (pt), cubic feet (ft³) and cubic yards (yd³).

A detailed list and conversion coefficients may be found in the appendix.

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