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The slant height of a right circular cone is the distance from any point on the circle of its base to the apex via a line segment along the surface of the cone. It is given by r 2 + h 2 {\displaystyle {\sqrt {r^{2}+h^{2}}}} , where r {\displaystyle r} is the radius of the base and h {\displaystyle h} is the height.
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.
The slant height of a right square pyramid is defined as the height of one of its isosceles triangles. It can be obtained via the Pythagorean theorem : s = b 2 − l 2 4 , {\displaystyle s={\sqrt {b^{2}-{\frac {l^{2}}{4}}}},} where l {\displaystyle l} is the length of the triangle's base, also one of the square's edges, and b {\displaystyle b ...
In geometry, a hypercone (or ... An example of such a cone would be an expanding sound wave as ... is the radius and is the slant height . Surface area, radius, and ...
The pyramid height is defined as the length of the line segment between the apex and its orthogonal projection on the base. Given that B {\displaystyle B} is the base's area and h {\displaystyle h} is the height of a pyramid, the volume of a pyramid is: [ 25 ] V = 1 3 B h . {\displaystyle V={\frac {1}{3}}Bh.}
An example of slant range is the distance to an aircraft flying at high altitude with respect to that of the radar antenna. The slant range (1) is the hypotenuse of the triangle represented by the altitude of the aircraft and the distance between the radar antenna and the aircraft's ground track (point (3) on the earth directly below the aircraft).
This formula can be derived by partitioning the n-sided polygon into n congruent isosceles triangles, and then noting that the apothem is the height of each triangle, and that the area of a triangle equals half the base times the height. The following formulations are all equivalent:
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.