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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.
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. Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10 −6 metre).
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
where S n − 1 (r) is an (n − 1)-sphere of radius r (being the surface of an n-ball of radius r) and dA is the area element (equivalently, the (n − 1)-dimensional volume element). The surface area of the sphere satisfies a proportionality equation similar to the one for the volume of a ball: If A n − 1 ( r ) is the surface area of an ( n ...
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.
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(near r.t.) 535 kg/m 3: LNG (at 20 °C) 0.534 g/cm 3: CRC (near r.t.) 0.534 g/cm 3: 4 Be beryllium; use: 1.85 g/cm 3: WEL (near r.t.) 1848 kg/m 3: LNG (at 20 °C) 1.8477 g/cm 3: CRC (near r.t.) 1.85 g/cm 3: 5 B boron; use: 2.34 g/cm 3: WEL (near r.t.) 2460 kg/m 3: LNG (at r.t.) 2.34 g/cm 3: CRC (near r.t.) 2.34 g/cm 3: 6 C carbon (graphite) use ...
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