About the Frustum
What Is a Frustum?
A frustum is the portion of a cone or pyramid that lies between two parallel planes cutting it. In the most common case, a conical frustum is created when a cone is sliced by a plane parallel to its base, removing the pointed top. The result is a shape with two circular bases of different sizes connected by a tapered lateral surface.
Volume Formula
The volume of a conical frustum is V = (1/3) x pi x h x (R² + Rr + r²), where R is the top radius, r is the bottom radius, and h is the height. This formula elegantly accounts for the varying cross-section of the frustum.
Surface Area
The lateral surface area is LSA = pi(R + r) x slant, where the slant height = sqrt((R-r)² + h²). The total surface area adds both circular base areas: TSA = LSA + piR² + pir². These formulas are essential for material estimation.
Applications
Frustums appear in many engineering and design contexts: buckets, lampshades, loudspeaker horns, architectural columns, and transition pieces in ductwork. Understanding frustum properties is crucial in manufacturing, fluid dynamics, and optical design.