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For a given volume, the right circular cylinder with the smallest surface area has h = 2r. Equivalently, for a given surface area, the right circular cylinder with the largest volume has h = 2r, that is, the cylinder fits snugly in a cube of side length = altitude ( = diameter of base circle). [8]
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.
Volume is a measure of regions in three-dimensional space. [1] ... Diagram showing how to measure volume using a graduated cylinder with fluid dram markings, 1926.
The equilateral cylinder is characterized by being a right circular cylinder in which the diameter of the base is equal to the value of the height (geratrix). [ 4 ] Then, assuming that the radius of the base of an equilateral cylinder is r {\displaystyle r\,} then the diameter of the base of this cylinder is 2 r {\displaystyle 2r\,} and its ...
Engine displacement is the measure of the cylinder volume swept by all of the pistons of a piston engine, excluding the combustion chambers. [1] It is commonly used as an expression of an engine's size, and by extension as an indicator of the power (through mean effective pressure and rotational speed ) an engine might be capable of producing ...
The condition of balance ensures that the volume of the cone plus the volume of the sphere is equal to the volume of the cylinder. The volume of the cylinder is the cross section area, times the height, which is 2, or . Archimedes could also find the volume of the cone using the mechanical method, since, in modern terms, the integral involved ...
The aforementioned volume of the cone is of the volume of the cylinder, thus the volume outside of the cone is the volume of the cylinder. Therefore the volume of the upper half of the sphere is 2 3 {\textstyle {\frac {2}{3}}} of the volume of the cylinder.
The Winchester bushel is the volume of a cylinder 18.5 in (470 mm) in diameter and 8 in (200 mm) high, which gives an irrational number of approximately 2150.4202 cubic inches. [4] The modern American or US bushel is a variant of this, rounded to exactly 2150.42 cubic inches, less than one part per ten million less. [5]