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The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]
A right circular cone and an oblique circular cone A double cone (not shown infinitely extended) 3D model of a cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex that is not contained in the base.
A tuff cone, sometimes called an ash cone, is a small monogenetic volcanic cone produced by phreatic (hydrovolcanic) explosions directly associated with magma brought to the surface through a conduit from a deep-seated magma reservoir. They are characterized by high rims that have a maximum relief of 100–800 meters (330–2,620 ft) above the ...
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.
A conical hill (also cone or conical mountain) is a landform with a distinctly conical shape. It is usually isolated or rises above other surrounding foothills, and is often of volcanic origin. Conical hills or mountains occur in different shapes and are not necessarily geometrically-shaped cones; some are more tower-shaped or have an ...
In geometry, a spherical sector, [1] also known as a spherical cone, [2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap.
In geometry, a frustum (Latin for 'morsel'); [a] (pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal.
Earth's inner core is the innermost geologic layer of the planet Earth. It is primarily a solid ball with a radius of about 1,220 km (760 mi), which is about 20% of Earth's radius or 70% of the Moon's radius. [1] [2] There are no samples of the core accessible for direct measurement, as there are for Earth's mantle. [3]