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PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
This is a list of volume formulas of basic shapes: [4]: 405–406 ... and are the semi-major and semi-minor axes' length; Sphere – , where is ...
Solid semi-ellipsoid of revolution around z-axis a = the radius of the base circle h = the height of the semi-ellipsoid from the base cicle's center to the edge
The semi -axis a is the ... The volumetric circumference of a spheroid is the circumference of a sphere of equal volume as the spheroid ... These formulas are ...
where A is the area enclosed by an ellipse with semi-major axis a and semi ... where SV is the surface volume of a 3-sphere and r is the ... The buckling formula: = ...
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 perimeter of a stadium is calculated by the formula = (+) where a is the length of the straight sides and r is the radius of the semicircles. With the same parameters, the area of the stadium is A = π r 2 + 2 r a = r ( π r + 2 a ) {\displaystyle A=\pi r^{2}+2ra=r(\pi r+2a)} .
The area A of any triangle is the product of its inradius (the radius of its inscribed circle) and its semiperimeter: =. The area of a triangle can also be calculated from its semiperimeter and side lengths a, b, c using Heron's formula: