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A cone and a cylinder have radius r and height h. 2. The volume ratio is maintained when the height is scaled to h' = r √ π. 3. Decompose it into thin slices. 4. Using Cavalieri's principle, reshape each slice into a square of the same area. 5. The pyramid is replicated twice. 6. Combining them into a cube shows that the volume ratio is 1:3.
For a circular bicone with radius R and height center-to-top H, the formula for volume becomes V = 2 3 π R 2 H . {\displaystyle V={\frac {2}{3}}\pi R^{2}H.} For a right circular cone, the surface area is
The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma), is a volume-specific quantity defined as the weight W divided by the volume V of a material: = / Equivalently, it may also be formulated as the product of density, ρ, and gravity acceleration, g: = Its unit of measurement in the International System of Units (SI) is newton per cubic metre (N/m 3), with ...
A number of different units (some only of historical interest) are shown and expressed in terms of the corresponding SI unit. Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams) and are thus not listed in this article.
The gram (10 −3 kg) is an SI derived unit of mass. However, the names of all SI mass units are based on gram, rather than on kilogram; thus 10 3 kg is a megagram (10 6 g), not a *kilokilogram. The tonne (t) is an SI-compatible unit of mass equal to a megagram (Mg), or 10 3 kg.
Bone density is often expressed in grams per square centimeter (g·cm −2) as measured by x-ray absorptiometry, as a proxy for the actual density. The body mass index is expressed in units of kilograms per square meter, though the area figure is nominal, being the square of the height.
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The gram (originally gramme; [1] SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one thousandth of a kilogram.. Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to the cube of the hundredth part of a metre [1 cm 3], and at the temperature of melting ice", [2] the defining temperature (≈0 °C) was later changed to 4 ...