Question

Explain the structure of cone.

Answer 1

Definition of cone:

A cone is three dimensional geometric shape that smoothly diminishes in thickness from a flat base to a point called the apex or vertex.

The following are the properties of cone:

1. It has one circular face.
2. It has zero edges.
3. It has one vertex.

Structure of cone:

1. The distance from the perpendicular vertex of the cone to the base of the cone is the height '$\mathit{h}$' of the cone.
2. The circular base has a measured value of radius '$\mathit{r}$'
3. Length of the cone from apex to any point on the circumference is called slant height '$\mathit{l}$' of the cone.

Based on these quantities, formulae are derived as follows:

1. $Slantheightl=\sqrt{h^2+r^2}$

1. $Lateralsurfacearea=\pi rl$
2. $Totalsurfacearea=Basearea+Lateralsurfacearea$

$=\pi r^2+\pi rl$

4. $Volume=\frac{1}{3}\pi r^{2}h$

The imaginary line joining the center of the base and the vertex is called the $\mathit{A}\mathit{x}\mathit{i}\mathit{s}$ of the cone.

Based on the angle formed by the axis with the base of the cone, two types of cones are formed:

1. Right circular cone: In this, the axis forms a right angle with the base. In short, the axis is

perpendicular to the base as shown in figure(a).

2. Oblique cone: In this, the axis forms an angle $\theta \ne {90}^{°}$ with the base of the cone.

Therefore, it looks like slanted or tilted cone as shown in figure(b).