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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.
This is sometimes called the "linear diameter", and equals the diameter of a flat, circular sheet of material, usually metal, which is the right size to be cut and bent to make the dish. Two intermediate results are useful in the calculation: P = 2 F (or the equivalent: P = R 2 / 2 D ) and Q = √ P 2 + R 2 , where F , D , and R are ...
1.84 × 10 5: Volume of gas in the USS Macon zeppelin 2.118 90 × 10 5: Volume of gas in the Hindenburg zeppelin: 6.50 × 10 5: Volume of crude oil that can be carried aboard the Knock Nevis supertanker: 9.66 × 10 5: Volume of Taipei 101's gross floor space [5] 1 × 10 ^ 6 m 3 (1,300,000 cu yd; 0.0010 km 3) One cubic hectometre, one gigalitre ...
A metric ounce is an approximation of the imperial ounce, US dry ounce, or US fluid ounce. These three customary units vary. However, the metric ounce is usually taken as 25 or 30 ml (0.88 or 1.06 imp fl oz; 0.85 or 1.01 US fl oz) when volume is being measured, or in grams when mass is being measured.
The two effects exactly cancel each other out. In the extreme case of the smallest possible sphere, the cylinder vanishes (its radius becomes zero) and the height equals the diameter of the sphere. In this case the volume of the band is the volume of the whole sphere, which matches the formula given above.
Volume may be measured either in terms of units of cubic length or with specific volume units. The units of cubic length (the cubic inch, cubic foot, cubic mile, etc.) are the same in the imperial and US customary systems, but they differ in their specific units of volume (the bushel, gallon, fluid ounce, etc.). The US customary system has one ...
In other words, a volume form gives rise to a measure with respect to which functions can be integrated by the appropriate Lebesgue integral. The absolute value of a volume form is a volume element, which is also known variously as a twisted volume form or pseudo-volume form. It also defines a measure, but exists on any differentiable manifold ...
Mathematically, density is defined as mass divided by volume: [1] =, where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume , [ 2 ] although this is scientifically inaccurate – this quantity is more ...