The slant height of a right circular cone is the distance from any point on the circle to the apex of the cone.
The slant height of a cone is given by the formula, where is the radius of the circle and is the height of a square
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, another leg will have length, and by the Pythagorean theorem, and 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.
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.
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:
- The vertical height (or altitude) which is the perpendicular distance from the top down to the base.
- The radius of the circular base
- The slant height which is the distance from the top, down the side, to a point on the base circumference.
Famous quotes containing the words slant and/or height:
“There’s a certain Slant of light,
Winter Afternoons—”
—Emily Dickinson (1830–1886)
“We have not the motive to prepare ourselves for a “life-work” of teaching, of social work—we know that we would lay it down with hallelujah in the height of our success, to make a home for the right man. And all the time in the background of our consciousness rings the warning that perhaps the right man will never come. A great love is given to very few. Perhaps this make-shift time filler of a job is our life work after all.”
—Ruth Benedict (1887–1948)