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PepsiCo introduced the first two-liter sized soft drink bottle in 1970. [1] Motivated by market research conducted by new marketing vice president John Sculley (who would later be known for heading Apple Inc. from 1983 to 1993), [2] the bottle and the method of its production were designed by a team led by Nathaniel Wyeth of DuPont, who received the patent in 1973. [3]
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
Double" shots (surprisingly not always the size of two single shots, even in the same place) are 40–100 ml (1.4–3.5 imp fl oz; 1.4–3.4 US fl oz). In the UK, spirits are sold in shots of either 25 ml (0.88 imp fl oz; 0.85 US fl oz) (approximating the old fluid ounce) or 35 ml (1.2 imp fl oz; 1.2 US fl oz). [41]
A 6-colored Klein bottle, the only exception to the Heawood conjecture. Six colors suffice to color any map on the surface of a Klein bottle; this is the only exception to the Heawood conjecture, a generalization of the four color theorem, which would require seven. A Klein bottle is homeomorphic to the connected sum of two projective planes. [7]
UK beer bottles are all one-trip, and most are 500 mL (16.9 U.S. fl oz; 17.6 imp fl oz) or 330 mL (11.2 U.S. fl oz; 11.6 imp fl oz) in volume. The compulsory high recycled-content of these bottles makes them very dark and the lack of temper makes them chip easily when being opened.
Fabric "weight" is often specified as mass per unit area, grams per square meter (gsm) or ounces per square yard. It is also sometimes specified in ounces per yard in a standard width for the particular cloth. One gram per square meter equals 0.0295 ounces per square yard; one ounce per square yard equals 33.9 grams per square meter.
The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere.
The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m −1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus