# Spherical Wedge And Spherical Lune Formula

## Spherical Wedge And Spherical Lune Formula

A spherical wedge is a solid that is created by rotating a semicircle less than 360 degrees around its circumference. The region on a sphere that is encircled by two half circles that cross at antipodal points is known as a spherical lune. When one refers to a point on a sphere’s surface as being antipodal, one indicates that it is directly opposite to it. A straight line will be formed if one draws a line connecting two points. Volume, arc length, and the surface area must be calculated when using the Spherical Wedge And Spherical Lune Formula. Lunes have only a curved surface area and a form that mimics a curve. A spherical lune is a region on a sphere that is bordered by two half-great circles that cross at antipodal points in spherical geometry. It is an illustration of a digon, with a dihedral angle.  The Latin word for Moon, luna, is where the term “lune” comes from. The greatest circles (circumferences) of a sphere can divide its surface into two equally sized halves; they are known as great circles. There are two polar opposite spots where two huge circles always intersect. Lines of longitude (meridians) on a sphere that intersect at the north and south poles are typical instances of great circles. There are two symmetry planes in a spherical lune. It can be divided into two right spherical triangles or two lunes of half the angle by an equatorial line. A hosohedron is a lunes-based tessellation of the sphere. An equatorial bisector can divide each hosohedron into two equal spherical triangles. The lit area of the Moon that can be seen from Earth is a spherical lune. The dividing line between the Moon’s dark and illuminated halves is the first of two intersecting great circles. A terrestrial terminator known as the second great circle divides the Earth’s visible and invisible halves. From Earth, the spherical lune appears as a bright crescent.

### Spherical Wedge and Spherical Lune Formula

An equivalent of a sphere is a spherical wedge, and an equivalent of a spherical surface is a spherical lune. The Spherical Wedge And Spherical Lune Formula are obtained using ratios and proportions. The Spherical Wedge And Spherical Lune Formula for the volume of a sphere per rotation are equal to the ratio of the wedge’s volume to its central angle. The Spherical Wedge And Spherical Lune Formula for the volume of the wedge are equal to two-thirds of the product of the radius’s cube and its central angle (in radians). The Spherical Wedge And Spherical Lune Formula for the area of a sphere every revolution is equal to the ratio of the lune’s area to its central angle. The product of the square of the radius and the central angle, multiplied by two, gives the area of a Spherical Wedge And Spherical Lune Formula (in radians). A spherical wedge, also known as an ungual in geometry, is a section of a ball surrounded by two planar semidisks and a spherical lune (also known as the wedge’s base). The dihedral is the angle between the radii located within the bounding semidisks. If AB is a semidisk that forms a ball when fully rotated around the z-axis, rotating AB solely via a specific angle results in a spherical wedge with the same angle. A spherical wedge is to the sphere of which it is a part as the angle of the wedge is to a perigon, according to Beman. According to Hart, “the number of degrees in the [angle of the wedge’s] is to 360 as the Spherical Wedge And Spherical Lune Formula for the volume of a spherical wedge is to the volume of the sphere.”

### Sample Problems

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