Total Surface Area of a Frustum
Total Surface Area of a Frustum
\[A = \pi(R^2 + r^2) + \pi(R + r)l\]
Variables
A = total surface area (m²)
R = radius of the larger base (m)
r = radius of the smaller base (m)
l = slant 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
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