Introduction to Cone

A cone is a solid figure generated by a line, one end of which is fixed and the other end describe a closed curve in a plane.

A circular cone is a solid figure whose base is a circle and whose lateral surface area (i.e. curved surface area) tapers uniformly to a point: which is called the vertex or apex. The axis of the cone is a straight line drawn from the vertex to the center of the base.


intro-cone

A right circular cone is a cone whose base is a circle and whose axis is perpendicular to the base. Such a cone can also be described as solid formed by a right triangle rotated about one of its sides as an axis; it may, therefore, be called a cone of revolution. Altitude of a cone is the perpendicular line from the vertex to the base. (OF as shown in the figure).

The slant height is the length of a straight line drawn from the vertex to the circumference of the base (CF as shown in the figure). If C is any point on the circle (base of the cone), we obtain by Pythagorean Theorem,

\begin{gathered} C{F^2} = O{C^2} + O{F^2} \\ CF = \sqrt {{r^2} + {h^2}} \\ l = \sqrt {{r^2} + {h^2}} \\ \end{gathered}

Where

CF = l, being slant height of the cone
OF = altitude of the cone
OC = r, radius of the base of the cone

A pyramid with a circular base is given the special name of cone i.e., a cone may be considered the limiting case of a pyramid when the number of sides of the base polygon increases indefinitely.

Comments

comments