# 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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