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On the Sphere and Cylinder (Greek: Περὶ σφαίρας καὶ κυλίνδρου) is a treatise that was published by Archimedes in two volumes c. 225 BCE. [1] It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder , and was the first to do so.
The dependence of the volume of the sphere on the radius is obvious from scaling, although that also was not trivial to make rigorous back then. The method then gives the familiar formula for the volume of a sphere. By scaling the dimensions linearly Archimedes easily extended the volume result to spheroids. [1]: 21-23
The increase in weight is equal to the amount of liquid displaced by the object, which is the same as the volume of the suspended object times the density of the liquid. [1] The concept of Archimedes' principle is that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. [2]
Archimedes gives the value of the square root of 3 as lying between 265 / 153 (approximately 1.7320261) and 1351 / 780 (approximately 1.7320512) in Measurement of a Circle. The actual value is approximately 1.7320508, making this a very accurate estimate.
The Archimedes number is applied often in the engineering of packed beds, which are very common in the chemical processing industry. [3] A packed bed reactor, which is similar to the ideal plug flow reactor model, involves packing a tubular reactor with a solid catalyst, then passing incompressible or compressible fluids through the solid bed. [3]
Archimedes' investigation of paraboloids was possibly an idealization of the shapes of ships' hulls. Some of the paraboloids float with the base under water and the summit above water, similar to the way that icebergs float. Of Archimedes' works that survive, the second book of On Floating Bodies is considered his most mature work. [6]
Consisting of 32 propositions, the work explores properties of and theorems related to the solids generated by revolution of conic sections about their axes, including paraboloids, hyperboloids, and spheroids. [1] The principal result of the work is comparing the volume of any segment cut off by a plane with the volume of a cone with equal base ...
Archimedes' principle (also spelled Archimedes's principle) states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. [1] Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of ...
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