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Slant height

 

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Slant height



 
 
The slant height of a right circular cone is the distance from any point on the circle
Circle

A circle is a simple shape of Euclidean geometry consisting of those






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The slant height of a right circular cone is the distance from any point on the circle
Circle

A circle is a simple shape of Euclidean geometry consisting of those point in a plane which are the same distance from a given point called the center....
 to the apex of the cone.

The slant height of a cone is given by the formula , where is the radius
RADIUS

Remote Authentication Dial In User Service is a networking protocol that provides centralized access, authorization and accounting management for people or computers to connect and use a network service....
 of the circle and is the height from the center of the circle to the apex of the cone.

It is trivial to see why this formula holds true. If a right triangle is inscribed inside the cone, with one leg of the triangle being the line segment
Line segment

In geometry, a line segment is a part of a line that is bounded by two end Point , and contains every point on the line between its end points....
 from the center of the circle to its radius, and the second leg of the triangle being 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
Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a triangle#Types of triangles....
, , and gives the length of the circle to the apex of the cone.