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Friday, December 2, 2022

Volume of Cone – Definition, Structure, Surface Area

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The space and the capacity of the cone are defined as the volume of cone. A cone is a three-dimensional figure which is punctured at the bottom of the base part to the apex or vertex. This cone is formed by a set of other line segments which are half-lines or the lines which are being connected to a common point, towards the apex. While the base point does not consist of the apex structure.

The non-congruent circular disks of the cone are stacked one another which is the ratio of the radius of the disks which is always the constant.

As known, a cone is defined as a circular cross-section structure that is shaped like a pyramid. While the right cone is defined as the cone which has a vertex above the central part of the base. This structure is called the right circular cone. A student can easily find the measurement of the cone if you know the height and radius and then the formula is then structured.

The volume of this 3D structure is the amount of space that is being occupied by the structure. Volume is measured in the measuring units which can be in cubic meters. The cubic meters can be in – in3, ft3, cm3, m3, in3, ft3, cm3, m3, etc. Also, the students should make sure that the measurements should be in the same unit before they compute the volume of the structure.

A cylinder, cone, pyramid, and prism are of a similar structure thus their volume measurement is related in some or another way.

What Are the Properties of Cone?

The properties of the cone are as follows:

  • A cone consists of only one face.
  • The face is a circular base that has no edges.
  • Volume of the Cone = ⅓ πr2h
  • Total Surface Area of the Cone = πr (l + r)
  • Slant Height of the Cone = √(r2+h2)

Some Perfect Examples of Cone

Examples of cone-like structures that we see in our daily life are as follows:

  • A party hat
  • An ice-cream cone
  • A funnel which is shaped like the cone
  • Traffic Cone
  • Waffle cone
  • A Christmas tree

All these structures resemble the conic figure which has only one face that is the base. Also, these structures’ volumes are being calculated with the help of the formula of the cone.

What is the Surface Area of Cone?

The surface area of the cone can be defined as the whole area which is being covered by the structure. So, what does the surface area of the cone cover? The surface area of cone covers the base area and the lateral structure of the cone. The cone at a point can also be viewed as a set of the non-congruent circular disks which are being placed on top of one another, this is so placed that the ratio of the radius of the adjacent disks is always the same

What will be the Formula for the Surface Area of the Cone?

As already mentioned, the surface area of the cone is the total area which is occupied by the surface in a 3D plane structure. The total surface area is always equal to the curved surface area and the circular base of the conic structure.

The surface area of the cone = πr(r+√(h2+r2)). In this case, ‘r’ is called the radius of the circular base of the cone, and ‘h’ is the height of the cone.

Another formula for the surface area of the cone = πr (r+ L)

Here, L is the slanted height of the cone structure.

The curved surface area of the cone will be πrl.

In this study, we have learned a great deal about cones. Visit Cuemath for more such amazing content on Maths.

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