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US hat size is the circumference of the head, measured in inches, divided by pi, rounded to the nearest 1/8 inch. This corresponds to the 1D mean diameter. [1] Diameter at breast height is the circumference of tree trunk, measured at height of 4.5 feet, divided by pi. This corresponds to the 1D mean diameter.
r is the radius of the sphere, h is the height of the cap, and; sr is the unit, steradian, sr = rad 2. Because the surface area A of a sphere is 4πr 2, the definition implies that a sphere subtends 4π steradians (≈ 12.56637 sr) at its centre, or that a steradian subtends 1/4π ≈ 0.07958 of a sphere.
≡ 1 ft/h = 8.4 6 × 10 −5 m/s foot per minute: fpm ≡ 1 ft/min = 5.08 × 10 −3 m/s: foot per second: fps ≡ 1 ft/s = 3.048 × 10 −1 m/s: furlong per fortnight: ≡ furlong/fortnight ≈ 1.663 095 × 10 −4 m/s: inch per hour: iph ≡ 1 in/h = 7.0 5 × 10 −6 m/s inch per minute: ipm ≡ 1 in/min = 4.2 3 × 10 −4 m/s inch per ...
For example, assuming the Earth is a sphere of radius 6371 km, the surface area of the arctic (north of the Arctic Circle, at latitude 66.56° as of August 2016 [7]) is 2π ⋅ 6371 2 | sin 90° − sin 66.56° | = 21.04 million km 2 (8.12 million sq mi), or 0.5 ⋅ | sin 90° − sin 66.56° | = 4.125% of the total surface area of the Earth.
S 1: a 1-sphere is a circle of radius r; S 2: a 2-sphere is an ordinary sphere; S 3: a 3-sphere is a sphere in 4-dimensional Euclidean space. Spheres for n > 2 are sometimes called hyperspheres. The n-sphere of unit radius centered at the origin is denoted S n and is often referred to as "the" n-sphere. The ordinary sphere is a ...
Cross-sectional area of a mechanical pencil lead (0.5-0.7 mm in diameter) [16] 10 −6: 1 square millimetre (mm 2) 1–2 mm 2: Area of a human fovea [17] 2 mm 2: Area of the head of a pin: 10 −5 30–50 mm 2: Area of a 6–8 mm hole punched in a piece of paper by a hole punch [18] 10 −4: 1 square centimetre (cm 2) 290 mm 2: Area of one side ...
Thus, the segment volume equals the sum of three volumes: two right circular cylinders one of radius a and the second of radius b (both of height /) and a sphere of radius /. The curved surface area of the spherical zone—which excludes the top and bottom bases—is given by =.
Diagram showing a section through the centre of a cone (1) subtending a solid angle of 1 steradian in a sphere of radius r, along with the spherical "cap" (2). The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A/2 and r = 1.