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Frustum of a Cone

The part of a cone that remains after it has been cut by a plane parallel to its base is known as the frustum. A frustum is described for cones and pyramids. This term refers to a truncated shape.

Introduction

The frustum is the part of a cone that persists once a plane parallel has cut it from its base. A frustum is defined as cones with pyramids. A frustum is a term used to describe a truncated form. Frustums come in various shapes, based on the form from which they are made.

  • Cone’s frustum
  • A triangular pyramid’s frustum
  • A square pyramid’s frustum, and many more

Let’s have a look at the frustum of a cone’s definitions, properties, volume, surface area, and examples. Let’s discuss the frustum of a cone in detail. 

What is Frustum of Cone?

The frustum is the part of a cone but without vertex separated into various portions by a plane parallel to the cone’s base. The frustum of a cone appears to be known as a truncated cone. The frustum of a cone, like every other 3D object, has surface area and volume. In the following sections, we’ll look at the formulas for identifying them. 

Net of Frustum of Cone

The net of any form is formed up of several two-dimensional shapes produced by releasing three-dimensional shapes; in these other terms, whenever the net of a frustum gets folded up, the matching frustum is made. Two circles equate to the circular base in the net of a cone’s frustum.

Properties of Frustum of Cone

Every method of a cone’s frustum has produced the properties of the frustum. The characteristics of the frustum of a cone are listed here.

  • The frustum of a cone doesn’t include the corresponding cone’s vertex but has the cone’s base.
  • The frustum of a cone is defined by its height, possibly two radii (corresponding to two bases).
  • The height of the frustum of the cone is determined by the perpendicular distance here between the centres of something like the two frustum bases.
  • If a cone appears to be right-circular, the frustums that form with it will also appear to be right-circular.

Frustum of a Cone Volume

The frustum volume of a cone seems to be the amount of space it includes. The volume of a cone’s frustum, like the capacity of any other form, is measured in cubic units like m3, cm3 ,in3, and so on. Suppose a cone with a radius R at the base and a height H + h. Consider that a frustum of a cone of height H is created from the cone, with a high base radius ‘R’ and a small base radius ‘r’. The slant heights of the frustum and the cones were L and L + l. The volume of the frustum of the cone can be calculated using one of the methods below. 

The volume of the frustum of a cone can then be calculated using one of the formulas below if you want to learn more about how you created this frustum of a cone formula. 

Frustum of a cone volume = πh/3 [ (R3 – r3) / r ] (OR)

 Frustum of a cone volume = πH/3 (R2 + Rr + r2)

Conclusion

We come across many objects in our daily lives that require us to determine their volume and surface areas. For instance, we may need to figure out how much water a tank can store. We’ll need to know the tank’s shape and how to estimate its volume to do so. Some solids are made up of several various standard forms. A frustum is a shape that remains after cutting off the little top cone. We’ve all seen this shape in our everyday lives; our drinking cups were shaped like this.