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The volume is 4 / 3 π r 3 for the sphere, and 2 π r 3 for the cylinder. The surface area is 4 π r 2 for the sphere, and 6 π r 2 for the cylinder (including its two bases), where r is the radius of the sphere and cylinder.
The power law is often used in wind power assessments [4] [5] where wind speeds at the height of a turbine ( 50 metres) must be estimated from near surface wind observations (~10 metres), or where wind speed data at various heights must be adjusted to a standard height [6] prior to use.
A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
The circle is the shape with the largest area for a given length of perimeter (see Isoperimetric inequality). The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O(2,R).
A drainage basin is an area of land in which all flowing surface water converges to a single point, such as a river mouth, or flows into another body of water, such as a lake or ocean. A basin is separated from adjacent basins by a perimeter, the drainage divide , [ 1 ] made up of a succession of elevated features, such as ridges and hills .
The multiple choice section is scored by computer, with a correct answer receiving 1 point, with omitted and incorrect answers not affecting the raw score. This total is multiplied by 1.2 to calculate the adjusted multiple-choice score. [26] The free response section is hand-graded by hundreds of AP teachers and professors each June. [27]
The method of exhaustion was later discovered independently in China by Liu Hui in the 3rd century AD to find the area of a circle. [12] [13] In the 5th century AD, Zu Gengzhi, son of Zu Chongzhi, established a method [14] [15] that would later be called Cavalieri's principle to find the volume of a sphere.