A cone is a three-dimensional geometric shape that narrows from a flat circular base to a single point called apex or vertex. In other words, a cone can be formed by joining an infinite number of slanting lines to the circumference of a circle from a single point called the vertex. The distance from the vertex of a cone to the centre point of the base is known as the height of the cone. The length of the cone from the vertex to the boundary of the circular base is known as the slanting height.
Types of a Cone
1. Right Circular Cone
If the axis of a cone forms a right angle with the circular base, then such a cone is called a right circular cone. In other words, if the axis line of a cone passes through both the vertex and the centre of the circular base or when the vertex of the cone lies directly above the centre of the circular base then such a cone is called the right circular cone.
2. Oblique Cone
If the axis of a cone does not form a right angle with the circular base, then such a cone is called an oblique cone. Hence, the axis line of an oblique cone does not pass through both the vertex and the centre of the circular base. In other words, when the vertex of the cone is not located directly above the centre of the circular base then such a cone is called an oblique cone. The oblique cones are slightly tilted in nature.
Properties of a Cone
1. A cone has only one face, which is the circular base.
2. A cone has no edges.
3. A cone has only one apex or vertex point.
Formulae related to a Cone
1. The volume of the cone is given as ⅓ πr²h.
2. The total surface area of the cone is calculated as πr(l + r).
3. The length of the slant height of the cone can be obtained by evaluating √(r²+h²).
Examples of a Cone
1. Ice Cream Cone
An ice cream cone is one of the best examples of the conical objects present around us. One can easily visualise an infinite number of slanting lines joining the vertex or the base of the cone and the circumference of a circle or the top of the cone.
2. Party Hat
A party hat also known as a birthday cap is yet another example of the conical objects used in everyday life. Similarly, the witch hat is also conical in shape.
3. Christmas Tree
Christmas trees are a classic example of conical structures available in nature. Similarly, one can also visualise cone geometric shape by looking at other trees such as deodar, sugar pine, red spruce, etc.
Funnels are yet another example of the common cone-shaped objects used in everyday life. The apex of the conical funnel is often attached to a cylindrical pipe that directs the flow of liquid and resists it from spilling.
Volcanos are one of the prime examples of cone-shaped objects existing in nature. The lava escapes out from the apex or the vertex of a volcano.
6. Traffic Cone
Traffic cones are also known as pylons or road cones. They are usually orange in colour and are painted with broad white stripes. The purpose of a traffic cone placed on the road is to redirect the traffic to ensure safety and avoid any mishap.
Some of the shells naturally occur in the shape of a cone. So if you pursue shell collecting as a hobby, you must have seen cone-shaped shells in real life.
8. Loud Speaker
A loudspeaker is used to convert the electrical signal into sound signal. The front side of a loudspeaker is usually attached with a conical plastic cup. The conical shape of the cup helps the consumer to direct sound energy in a particular direction. Hence, a loudspeaker or a megaphone is a suitable example of cone-shaped objects used in everyday life.
Some of the vegetables such as a carrot, raddish, corn, etc. closely resemble the cone geometric shape. Hence, one can easily visualise the conical geometric shape by looking at such vegetables.
10. Top of a Rocket
The top of a Rocket or an airplane is designed in the shape of a cone. The conical shape of the top helps the vehicle to reject or minimize the air resistance and take-off smoothly.
11. Drinking Glass
Martini or cocktail drinking glasses are usually shaped like an inverted cone. The apex of the conical cocktail glass is attached with a cylindrical rod that is further fixed to a circular disk forming the base of the glass.
12. Sharpened End of a Pencil
If you look at the tip of a properly sharpened pencil, you can easily visualise the conical geometric shape because it consists of a single vertex and a circular base.
13. Icing on the Top of a Cupcake
The icing placed on the top of a cupcake is generally shaped like a cone.
14. Top of a Temple
The top of a temple also known as the ‘shikara’ or ‘shikhara’ is usually shaped like a cone. Hence, it forms a perfect example of conical objects present around us.
Tepee or tipi is a conical tent used by hikers. The curved surface of a tipi is made up of fabric, plastic, or canvass. Hence, it is yet another example of cone-shaped objects used in real life.
16. Fountain Firecrackers
Fountain firecrackers are a prominent example of conical objects used in everyday life.
17. Stack-a-Ring Toy
A stack-a-ring toy with all the rings stacked in ascending order from top to bottom forms a classic example of cone-shaped objects present in real life.
18. Rice Hat
Rice hat is an Asian traditional hat also known as coolie hat. It is quite popular in southeastern parts of Asia. It is conical in shape. Hence, they constitute a perfect example of cone-shaped objects used in everyday life.
19. Russian Dolls
Matryoshka doll or the Russian dolls is a representation of Russian culture. Some of these dolls are conical in shape.
20. Paper Cup
Some of the paper cups are shaped like a cone. Such cups are suitable for quick drinking. Also, conical paper cups are easy to hold and drink from. The only limitation of using a conical paper cup is that they cannot be placed on a flat surface.