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The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
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.
Using radians, the formula for the arc length s of a circular arc of radius r and subtending a central angle of measure 𝜃 is =, and the formula for the area A of a circular sector of radius r and with central angle of measure 𝜃 is A = 1 2 θ r 2 . {\displaystyle A={\frac {1}{2}}\theta r^{2}.}
The diameter or metric diameter of a subset of a metric space is the least upper bound of the set of all distances between pairs of points in the subset. Explicitly, if S {\displaystyle S} is the subset and if ρ {\displaystyle \rho } is the metric , the diameter is diam ( S ) = sup x , y ∈ S ρ ( x , y ) . {\displaystyle \operatorname ...
The next wire size thicker than 4/0 has a cross section of 250 kcmil. A circular mil is the area of a wire one mil in diameter. One million circular mils is the area of a circle with 1,000 mil (1 inch) diameter. An older abbreviation for one thousand circular mils is MCM.
The basal area (BA) of a tree can be estimated from its diameter at breast height (DBH), the diameter of the trunk as measured 1.3m (4.5 ft) above the ground. DBH is converted to BA based on the formula for the area of a circle:
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry , a circular segment or disk segment (symbol: ⌓ ) is a region of a disk [ 1 ] which is "cut off" from the rest of the disk by a straight line.