What is Cone?
A cone is a three dimension solid object that has a circular base joined to point by a curved side and one vertex. Here, you will learn The Right Circular Cone | Properties of Cone.
Type of Cone:
There is two type of cone:
1. Right Circular Cone
2. Oblique Cone
A cone which has a circular base but the axis of the cone is not perpendicular with the base, is called an Oblique cone.
Right Circular Cone
A right circular cone is a solid generated by the revolution of a right-angled triangle about one of the side containing the right angel.
Slant height of a right circular cone is the distance of its vertex from any point on the circumference of the base i.e l is slant height.
If r, h and l is denoted radius, height and slant height of right Circular Cone then:
Volume of Right Circular Cone
The volume of the right circular cone is equal to one-third the product of the base area and the height.
V=13 x (π × r2 x b x h
Volume = 13πr2h
Curved surface Area= πrl
Total surface Area= πr(r + l)
Properties of Right Circular Cone
• All elements of a right circular cone are equal.
• A section of a right circular cone that contains the vertex and two points of the base is an isosceles triangle.
• A right circular cone is a circular cone whose axis is perpendicular to its base.
• A cone has only one face, which is the circular base but no edges or vertices.
• A cone has only a vertex point.
Frustum of a Cone
If a one is cut by a plane parallel to the base of the cone then the portion between the pane and base is known as Frustum of a Cone.
Slant height l2 = h2 + (R-r)2
Volume = πh3(R2 + r2 + Rr)
Curved surface Area= πl(R + r)
Total surface Area= π(R2 + r2 + l(R + r))
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