Frustum of a Cone Lateral (or Curved) Surface Area

The entire surface area of a frustum equals the sum of its faces. First, let’s define a frustum before looking at the formula for estimating its surface area. A frustum is a chopped-off piece of a pyramid or cone that runs parallel to the Base and is sliced off by a plane. A frustum is a term used to describe a truncated shape. On the other hand, The segment of a right circular cone between the Base and just a section parallel to the Base, which does not pass through into the vertex, is the frustum. The perpendicular distance between any two bases is the altitude of a total surface area of the frustum of a right circular cone. 

What Is a Frustum of a Right Circular Cone?

A region of a right circular cone surrounded by its Base, a section parallel to the Base, and the conical surface included between the base of the cone and the parallel section is known as the frustum. Different areas make up a circular cone’s frustum. The various elements of a right circular cone’s frustum are listed below.

Lower Base – a base of a right circular cone’s frustum with a greater radius. 

Upper Base – a base of a right circular cone’s frustum with a smaller radius. 

Altitude – the distance here between bases of a cone’s frustum on a perpendicular plane. 

Slant Height – the distance determined along the frustum’s lateral face

Radii – The distance between a base’s centre and its edge

Properties of Frustum of Cone

The qualities of a cone’s frustum were determined by how it is obtained from the cone. The qualities of a cone’s frustum are listed below.

• The frustum of a cone does not include the corresponding cone’s vertex, but it does contain the cone’s Base.

• The height or two radii of such a cone define its frustum (corresponding to two bases).

• The perpendicular distance between the centres of the two frustum bases depends on the height of the frustum of the cone.
• If the cone is right-circular, the frustums that develop will also be right-circular.

Surface Area of Frustum of Cone

The frustum area is calculated by adding the areas of all the cone’s faces. Since it is an area, it is calculated in square units, including m², cm², in², etc. There are two kinds of areas in the frustum of a cone.

Curved Surface Area (CSA) (or) Lateral Surface Area (LSA): This would be the area of the frustum’s curved surface.

Total Surface Area (TSA): This is the total area of all its faces (CSA + Sum of Areas of Circular Bases).

Consider a cone with just an R radius at the Base, a slant height of L + l, a height of H + h, and a slant height of L + l. Suppose the cone seems to have a height of H, a small base radius of r, an adequate base radius of R, and just a slant height of L. These are all the formulas for computing a cone frustum’s curved surface area or total surface area.

The frustum of a cone’s curved surface area gives,

 πl [ (R² – r²) / r ]

(OR) 

πL (R + r) = Curved Surface Area (or) Lateral Surface Area of a frustum of a cone

Surface Area of Frustum Formula

The lateral or frustum of a cone area of a curved surface might be calculated using the bases’ perimeters (or circumferences) and the slant height. The lateral (or curved) surface area of a frustum appears to be calculated using the following formula:

Lateral surface area = (1/2) × (C1 + C2) × L where

C1 – One of the frustum’s bases’ circumference. 

C2 – Another base of the frustum’s circle

L = the frustum’s slant height

To get the overall surface area, add the areas of both bases and the lateral (or curved) surface area of each frustum. i.e.,

Area of bases + Lateral (or curved) surface area = Total surface area (TSA) 

Conclusion

A cone is a solid with a simple closed curve around its Base or even a curved surface that tapers to the vertex opposite the Base. The Base of a cone is a circular cone if it is round. The perpendicular height, and height of a cone, is the distance between both the vertex and the base of a cone. A right circular cone’s slant height is the distance between the vertex and the Base’s circumference. The frustum of such a solid appears to be the portion of the solid that remains between the parallel cutting plane and the Base of a cone or pyramid. The Latin term frustum implies ‘piece’ and ‘crumb.’ I hope now you got all the necessary information regarding the total surface area of a frustum of a right circular cone.