Knowing the irregular object volume and its weight, he could calculate the density and compare it with the density of pure gold. From this observation, he deduced that volume of water displaced must be equal to the volume of the part of his body he had submerged. The idea came to him when he was taking a bath - stepping into a bathtub, he noticed that the water level rose. If it's an irregular shape, you can try to do the very thing that caused Archimedes to shout the famous word Eureka! Probably you heard that story - Archimedes was asked to find out if the Hiero's crown is made from pure gold or just gold-plated - but without bending or destroying it. For a right triangular prism, the equation can be easily derived, as well as for a right rectangular prism, which is apparently the same shape as a box.įor regular three-dimensional objects, you can easily calculate the volume by taking measurements of its dimensions and applying the appropriate volume equation. Prism = A h Ah A h, where A A A is a base area and h h h is the height. For a pyramid with a regular base, another equation may be used as well: Pyramid = ( n / 12 ) h s 2 cot ( π / n ) (n/12) h s^2 \cot(\pi/n) ( n /12 ) h s 2 cot ( π / n ), where n n n is a number of sides s s s of the base for a regular polygon. Pyramid = ( 1 / 3 ) A h (1/3)Ah ( 1/3 ) A h where A A A is a base area and h h h is the height. Rectangular solid (volume of a box) = l w h lwh lw h, where l l l is the length, w w w is the width and h h h is the height (a simple pool may serve as an example of such shape). Sphere = ( 4 / 3 ) π r 3 (4/3)\pi r^3 ( 4/3 ) π r 3, where r r r is the radius.Ĭylinder = π r 2 h \pi r^2h π r 2 h, where r r r is the radius and h h h is the height.Ĭone = ( 1 / 3 ) π r 2 h (1/3)\pi r^2h ( 1/3 ) π r 2 h, where r r r is the radius and h h h is the height. Here are the formulas for some of the most common shapes:Ĭube = s 3 s^3 s 3, where s s s is the length of the side. Quart (US) to Gallon (US) Conversion Table Quart (US) ġ5 qt (US) = 15 × 0.25 gal (US) = 3.There is no simple answer to this question, as it depends on the shape of the object in question. The imperial gallon is used even more sparingly than the US gallon, with most countries around the world using liters when referencing fuel. Gallons are also widely used in fuel economy expression in the US, as well as some of its territories. History/origin: The term gallon most closely originates from "galon" in Old Northern French and developed as a system for measuring wine and beer in England, resulting in measures such as the wine gallon, ale gallon, and imperial gallon.Ĭurrent use: In the United States (US), gallons are often used for larger containers, such as half gallon tubs of ice cream or one-gallon cartons of milk. A US fluid ounce is therefore 1/128 of a US gallon while an imperial fluid ounce is 1/160 of an imperial gallon. Further differentiating the US and the imperial gallon, a US gill is divided into four fluid ounces, while an imperial gallon is divided into five. A cup is comprised of two gills, making one gallon equal four quarts, eight pints, sixteen cups, or thirty-two gills. Quarts are then divided into two pints and pints are divided into two cups. In both systems, the gallon is divided into four quarts. In contrast, the imperial gallon, which is used in the United Kingdom, Canada, and some Caribbean nations, is defined as 4.54609 liters. The US gallon is defined as 231 cubic inches (3.785 liters). Gallon (US)ĭefinition: A gallon is a unit of volume specifically regarding liquid capacity in both the US customary and imperial systems of measurement. This same definition was used for the imperial quart up until 1824 when the UK re-defined the imperial gallon.Ĭurrent use: The respective versions of the quart are used mainly in the United States and the United Kingdom, though in the UK, the use of the liter is now mandated as a result of metrication. The current definition of the US quart is based on the English wine gallon. History/origin: The quart is based on the gallon, the definition of which has changed throughout history based on the commodity being referenced. In both the UK and the US, the quart is equal to ¼ of its respective gallon. In the UK, the imperial quart is equal to 1.136523. In the US, a liquid quart is equal to approximately 0.946353 liters and a dry quart is equal to approximately 1.101221 liters. Definition: The quart (symbol: qt) is a unit of volume in the United States customary and imperial systems of measurement.
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