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Measurement of volume by displacement, (a) before and (b) after an object has been submerged. The amount by which the liquid rises in the cylinder (∆V) is equal to the volume of the object. In fluid mechanics, displacement occurs when an object is largely immersed in a fluid, pushing it out of the way and taking its place. The volume of the ...
Some SI units of volume to scale and approximate corresponding mass of water. To ease calculations, a unit of volume is equal to the volume occupied by a unit cube (with a side length of one). Because the volume occupies three dimensions, if the metre (m) is chosen as a unit of length, the corresponding unit of volume is the cubic metre (m 3).
The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.
The aquarium was constructed from 41 acrylic panels – 26 panels for the outside cylinder and 15 panels for the inside cylinder for the elevator – which were bonded together on site. [7] With a diameter of about 11 m (36 ft) and a height of about 16 m (52 ft), resting on a 9 m (30 ft) tall foundation, it held the Guinness World Record for ...
Practical limitations, most notably the weight of water (1 kilogram per litre (8.345 lb/U.S. gal; 10.022 lb/imp gal)) and internal water pressure (requiring thick glass siding) of a large aquarium, restrict most home aquaria to a maximum of around 1 cubic metre in volume (1000 L, weighing 1,000 kg or 2,200 lb). [47]
The shell method goes as follows: Consider a volume in three dimensions obtained by rotating a cross-section in the xy-plane around the y-axis. Suppose the cross-section is defined by the graph of the positive function f(x) on the interval [a, b]. Then the formula for the volume will be: ()
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Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities