Frustum of a Cone-Lateral Surface Area

A cone is defined as a solid figure with a three-dimensional structure that has a circular base at the bottom of that cone. A cone has two surfaces, one is the “circular based area” and the other is the “lateral or the curved surface area”. Thus, “the surface area” of a frustum of a cone has a curved face. The “lateral surface area” of a frustum is a sum of the area of all sides of the frustum.

Frustum of a Cone “Lateral surface area”

A right frustum is equal to the cut part of the right angle cone. A frustum becomes circular when the base of a cone is circular. The height of the frustum has a perpendicular distance between the planes of the bases of that figure. During the calculation of the lateral “surface area” of a frustum, one can write about the area of a frustum in terms of the radius and the height. The “surface area” of a frustum is a total sum of an area of all faces of the cone. The Frustum of a cone is a part of a cone with the base of the cone which is cut by its plane that is parallel with its base. In a frustum of a cone the upper part of that cone remains the same and with its shape but the bottom part of that cone makes a “Frustum”. To get a proper frustum, one has to slice it parallel or horizontally to the base. Both slices have different areas and volumes. Mainly the “surface area” of a frustum is the sum of all areas of the bases of the cone. The cone lateral “surface area” of a frustum is measured by the units of cm2, m2, in2, etc. In a frustum there are two types of “surface area”, one is “Curved surface area” or “lateral surface area” and the second one is “Total surface area”. 

What is the Frustum of a Cone “Lateral surface area”?

The curved or “lateral surface area” of a cone or frustum is an area of the curved faces of a cone. The total “surface area” of a frustum of a pyramid or a cone is the total area of a total faces of the frustum of the cone. The “lateral surface area” or “curved surface area” is the area of its curved face. The height of the frustum of a cone is denoted by the ‘h’ and the radius 1 is denoted by the ‘R’ and the second radius is defined by the base ‘r’ and the slant height of the frustum is denoted by the ‘S’. There are two types of cone- “Right circular cone” and the “Oblique cone”. In general, people choose the right circular cone for any calculation regarding the frustum of a cone. The area of the surface of the frustum of a cone is the “curved surface area” of a frustum. On the other hand, a “total surface area” of a frustum of a right circular cone is the sum of the “lateral surface area” and the total area of the two bases.

How to find the “lateral surface area” of a frustum of a cone

The formula that is used to determine the “lateral surface area” of a frustum of a cone is given below:

“S = π * (r1 + r2) * l”

In this equation S denotes the “lateral surface area” of a frustum of a cone, π denotes the ratio of 22 and 7, and r1 and r2 denote the radii of the two parallel circular faces of the frustum of the cone. Here l denotes the slant height of the frustum of the cone. The slant height can be framed as:

“l = √ ((r1 – r2)2 + h2)” 

Here r1 and r2 are the two different radii and the actual height of the frustum of the cone.

Conclusion

There are some different types of the frustum; some of them are truncated pyramid, square pyramid, triangular pyramid, etc. A frustum depends on its height, base radius 1, and base radius 2. A frustum is also defined as a headless or truncated shape. So, the other name of this type of cone is “Truncated cone”. The frustum of a cone looks like a 3D shape. The volume of a cone is the middle solid space that is occupied by the cone itself. The two parts of a cone frustum are the top cut part and the base part of the cone. Thus, it can be concluded that the “Frustum of a Cone Lateral surface area” plays an important role in geometry.