Introduction

In our every day life , we come across objects like an ice-cream cone, a conical tent, a conical vessel, a clown's cap, a tapered end of a pencil etc. All these objects area conical in shape.

A right circular cone is a solid generated by revolving a line segment which passes through a fixed point and which makes a constant angle with a fixed line.

Vertex The fixed point V is called the vertex of the cone

Axis The fixed line VO is called the axis of the cone.

Base A right circular cone has a plane end , which is in circular shape. This is called the base of the cone.

Height The length of the line segment joining the vertex to centre of the base is called ,the height of the cone

Slant Height The length of the line segment joining the vertex to any point on the circular edge of the base is called ,the slant height of the cone.

Radius The radius of base circle is called the radius of the cone.

Consider a right circular cone of height h,slant height l and radius r as shown in fig.

clearly

By , Pythagoras Theorem , we have VA² = OA² + VO²

i.e. l² = r² + h²

i.e. l = √(r² + h²)

Curved Surface Area or lateral surface Area = r l

Total Surface Area = r l + r²

= r ( l + r)

Volume of a cone = 1/3 r²h