What happens to the frustum formula if r = 0?

If r = 0, you get a cone: V = (πh/3)R², which makes sense geometrically.

Is the slant height the same as the lateral surface area edge?

Yes, the slant height l is the length along the slanted edge of the frustum surface.

How is a frustum created?

Cut a cone with a plane parallel to the base, removing the top point. What remains is the frustum.

Mathematics

Frustum Calculator

Frustum Calculator (Truncated Cone)

Top Radius (r)

Bottom Radius (R)

Height (h)

A frustum is a truncated cone — a cone with the top cut off by a plane parallel to the base. It appears in architecture (towers, buckets) and engineering (funnels, lampshades).

Symbol	Name	Unit	Description
R	base radius (large)	length	—
r	top radius (small)	length	—
h	height	length	—
l	slant height	length	—
V	volume	length³	—

R	r	h	Volume
5	3	8	410.5
10	5	12	2199.1
8	4	10	1340.4
6	2	15	1319.5

References

›Frustum — Wolfram MathWorld

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Frustum Calculator (Truncated Cone)