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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. These objects bring to our mind the concept of a right circular cone, which may be defined as follows:
Right Circular Cone:
A right circular cone is a three-dimensional figure that is generated by rotating a right triangle about one of its legs.
The base is a circle; the slant height, l, is the hypotenuse of the triangle; the height, h, is one leg of the triangle, and the radius, r, is the other leg.
Vertex:
The fixed point V is called the vertex of the cone.
Axis:
The fixed 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.
O is the centre and OA is the radius of the circular base of the cone. The vertex of a right circular cone is farthest from its base.
Height:
The length of the line segment joining the vertex to the centre of the base is called the height of the cone.
length VO is 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.
lengths VA and VB are slant heights of the cone.
Radius:
The radius OA of the 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, \(\angle{VOA}\) = 90°. By pythagoras theorem we have,
\(VA^2 = OA^2 + VO^2\)
=> \(l^2 = r^2 + h^2\)
=> l = \(\sqrt{r^2 + h^2}\)
This is a relation between the height, slant height and radius of a right circular cone.
Net for a Cone:
