\[A = \pi(R^2 + r^2) + \pi(R + r)l\]
Variables
Atotal surface area (m²)
Rradius of the larger base (m)
rradius of the smaller base (m)
lslant height of the frustum (m)
Description
What is this formula?
This formula calculates the total surface area of a frustum of a cone, including both circular bases and the curved lateral surface.
When to use it
Use this formula when determining the full external surface area of truncated conical objects.
Example
If a frustum has:
R = 5 m
r = 2 m
l = 6 m
A = π(25 + 4) + π(7)(6)
A = 29π + 42π
A = 71π ≈ 223.30 m²
Applications
- Geometry and mathematics
- Engineering design
- Manufacturing
- Construction materials estimation
- Industrial modeling