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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 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 ...
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 tun is approximately the volume of a cylinder with both diameter and height of 42 inches, as the gallon was originally a cylinder with diameter of 7 inches and height of 6. [nb 3] The Queen Anne wine gallon of 231 cubic inches was adopted in 1707, and still serves as the definition of the US gallon.
An especially common rental cylinder provided at tropical dive resorts is the "aluminium-S80" which is an aluminum cylinder design with an internal volume of 0.39 cubic feet (11.0 L) rated to hold a nominal volume of 80 cubic feet (2,300 L) of atmospheric pressure gas at its rated working pressure of 3,000 pounds per square inch (207 bar). [9]
Reprint of 1935 edition. A problem on page 101 describes the shape formed by a sphere with a cylinder removed as a "napkin ring" and asks for a proof that the volume is the same as that of a sphere with diameter equal to the length of the hole. Pólya, George (1990), Mathematics and Plausible Reasoning, Vol.
Volume is a measure of regions in three-dimensional space. [1] ... Proof without words that the volume of a cone is a third of a cylinder of equal diameter and height ...
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 rounded to exactly 2150.42 cubic inches, a difference of less than one part per ten million. [5]