We have to use more elaborate methods to measure the volume of a gas. So, if you want to measure an irregular object's volume, just follow in Archimedes' footsteps (though you can omit the naked race part): Legend says that Archimedes was so excited about this discovery that he popped out of his bathtub and ran naked through the streets of Syracuse. Knowing the irregular object's 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. Liter to Cup (US) Conversion Table Liter ġ5 L, l = 15 × 4.2267528377 cup (US) = 63.There is no simple answer to this question, as it depends on the shape of the object in question. Standardized measuring cups are used instead. Actual drinking cups can vary significantly in terms of size and are generally not a good representation of this unit. customary teaspoons.Ĭurrent use: The cup is typically used in cooking to measure liquids and bulk foods, often within the context of serving sizes. One United States customary cup is equal to 236.5882365 milliliters as well as 1/16 U.S. ![]() ![]() The metric cup is defined as 250 milliliters. Cup (US)ĭefinition: A cup is a unit of volume in the imperial and United States customary systems of measurement. It is also used to measure certain non-liquid volumes such as the size of car trunks, backpacks and climbing packs, computer cases, microwaves, refrigerators, and recycling bins, as well as for expressing fuel volumes and prices in most countries around the world. However, due to the mass-volume relationship of water being based on a number of factors that can be cumbersome to control (temperature, pressure, purity, isotopic uniformity), as well as the discovery that the prototype of the kilogram was slightly too large (making the liter equal to 1.000028 dm 3 rather than 1 dm 3), the definition of the liter was reverted to its previous, and current definition.Ĭurrent use: The liter is used to measure many liquid volumes as well as to label containers containing said liquids. History/origin: There was a point from 1901 to 1964 when a liter was defined as the volume of one kilogram of pure water under the conditions of maximum density at atmospheric pressure. One liter is equal to 1 cubic decimeter (dm 3), 1,000 cubic centimeters (cm 3), or 1/1,000 cubic meters (m 3). Definition: A liter (symbol: L) is a unit of volume that is accepted for use with the International System of Units (SI) but is technically not an SI unit.
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