A circular truncated cone is a geometric solid composed of a cone and a circular truncated surface parallel to the base. The base of the circular truncated cone is a circle, and the top is a smaller circle. The lateral surface is a curved surface connecting the base and the top. The circular truncated cone can be described as a solid formed by rotating a right trapezoid around its vertical axis, which is perpendicular to the base.

The formula for the area of a truncated circular cone is S = π × (r’² + r² + r’l + rl), where r is the radius of the base, r’ is the radius of the apex and l is the oblique height. The lateral area of the truncated circular cone can be considered as the difference between the areas of two sectors.

The calculation of the surface area of a circular truncated cone is very useful in production, as it can be used to determine the amount of materials required for painting, wallpapering, tiling, and so on. For instance, if one needs to paint a circular truncated cone with a base radius of 5cm, a top radius of 3cm, and a slant height of 8cm, it is necessary to know its surface area (the surface area is S = π × (3² + 5² + 3×8 + 5×8) = 157.08cm²), in order to calculate the amount of paint needed.

Suggested reading materials include: “Formula for the Area of an Annulus,” “Formula for the Surface Area of a Cone,” “Formula for the Surface Area of a Cylinder,” “Formula for the Surface Area of a Circular Truncated Cone,” and “Formula for the Lateral Area of a Circular Truncated Cone.”