Cone Formulas for Competitive Exams

What is Cone?

A cone is a three-dimensional figure in
geometry that narrows smoothly from a flat base (usually circular base) to a
point(which forms an axis to the centre of the base) called the apex or vertex.
 The real-life example is a birthday cap
in the shape of a cone. We can also define the cone as a pyramid which has a
circular cross-section, unlike pyramid which has a triangular cross-section.
These cones are also stated as a circular cone.

Types of Cone

As we have
already discussed a brief definition of the cone, let’s talk about its types
now. Basically, there are two types of cones;

1. Right Circular Cone
2. Oblique Cone
   
   

Right Circular Cone

A cone which
has a circular base and the axis from the vertex of the cone towards the base
passes through the center of the circular base. The vertex of the cone lies
just above the center of the circular base. The word “right” is
used here because the axis forms a right angle with the base of the cone or is
perpendicular to the base. This is the most common types of cones which are
used in geometry. See the figure below which is an example of a right circular
cone.

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. The vertex of this cone is not located
directly above the centre of the circular base. Therefore, this cone looks like
a slanted cone or tilted cone.

Cone Formulas
1. Cone surface area = πr²+πrl
or

surface area of a cone = πr (l + r)

2. Slant Height, l = √(r²+h²)

3. Volume of the Cone, Volume(V)
= ⅓ πr²h
cubic units

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