How to Calculate the Dimensions, Area, Volume of Different Kinds of Cones?

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A Cone has three proportions, a solid assembly, and a base that is round in shape. A cone can also be defined as a structure that has disks placed on top of each other, having the shape of a circle and non -congruent in nature. The ratio of the radius of the disks adjacent to each other remains persistent.

A cone can also be thought of as a triangle that alternates around one of its apexes. Now, imagine a condition where you have to paint the faces of a conical flask. Before you start painting anything, you need to calculate the quantity of paint that would be required to cover the walls. You must know the area of each face of the flask so that you can determine the amount of paint every face need. this is what is called the total surface area. The sum of all the faces of a cone is called its total surface area of cone

Surface area is considered as the area that the surface of the cone occupies in the three-dimensional space. The sum includes the base area and the lateral area of a cone.

The formula for calculating the total surface area of cone is as follows:

When we combine the curved surface area and the base area of the cone, we get the total surface area of a cone. So, the calculation formula would be as follows:

                           TSA of cone = base area + curved surface area

The base of the surface of a cone is flat and round, it has a shape of a circle. So, the calculation formula is πr2 square units. It is known as the base surface area.

There are two kinds of cones:

  1. Right Circular Cone: A right angle is formed at the base and the axis of the cone. While studying geometry, commonly this kind of cone is used.
  1. Oblique Cone: This kind of cone has a base that is circular in shape, the vertex of which is situated above the circular base, but not directly in the center.

We also have to calculate the frustum of a cone; we get it when we cut a right circular cone in a manner where the cone that is original and the plane on which we cut it is parallel. So, both the ends have circular bases, at a different radius.

The glass for drinking water is an example of the frustum. For calculating the total surface area of the frustum, we add the areas of both these surfaces that are circular to the surface area of the frustum that is curved.  

Here is the list of cones that you usually see around you:

  • Birthday Caps for kids
  • Road barriers
  • The chemistry labs have flasks, which have a shape of a cone 
  • Funnels used for pouring oils into bottles
  • Cones used for ice-creams

You all can surely relate to all the objects mentioned above, they have a base that is flat and the other end is pointed, they are known as the apex and vertex of a cone. A cone is essentially shaped by line segments or lines that connect the vertex to all the places in the circular base that do not comprise the apex. The height of a cone is the distance from the base to the vertex of a cone. The radius of the base at the circle is measured. The slanting height of the cone is also calculated when you measure the length from the vertex to any place on the circumference of the circular base.

Considering the above details, we can easily arrive at the formulas for curved surface area, total surface area, and volume of cone.

You must practice a lot of questions to understand the chapter well. Cuemath provides you the best explanations related to the topic and helps you solve any problem with ease.

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