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| The '''slant height''' of a [[right circular cone]] is the distance from any point on the [[circle]] to the apex of the cone.
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| The slant height of a cone is given by the formula <math>\sqrt{r^2+h^2}</math>, where <math>r</math> is the [[radius]] of the circle and <math>h</math> is the height of a square
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| If the [[line segment]] from the center of the circle to its radius is taken as one leg of a [[right triangle]] inscribed within the cone, and the second leg of the triangle runs from the apex of the cone to the center of the circle, then one leg will have length <math>r</math>, another leg will have length <math>h</math>, and by the [[Pythagorean theorem]], <math>r^2+h^2=d^2</math>, and <math>d=\sqrt{r^2+h^2}</math> gives the length of the circle to the apex of the cone. This application is primarily useful in determining the slant height of a cone when given other information regarding the radius or height.
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| The variety of geometric implications of the slant height has made it a commonly seen factor in the mathematical community for 3-d geometric study.
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| A cone is defined primarily by three central aspects, with which one can determine any one factor given the other two. They are as follows:
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| *The vertical height (or altitude) which is the perpendicular distance from the top down to the base.
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| *The radius of the circular base
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| *The slant height which is the distance from the top, down the side, to a point on the base circumference.
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| ==References==
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| *[http://www.mathopenref.com/coneslantheight.html Slant height of a right cone] at Math Open Reference
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| [[Category:Geometric measurement]]
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| {{elementary-geometry-stub}}
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Latest revision as of 15:07, 24 September 2014
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