Volume of a Frustum of a Cone
Volume of a Frustum of a Cone
\[V = \frac{1}{3}\pi h(R^2 + Rr + r^2)\]
Variables
V = volume (m³)
R = radius of the larger base (m)
r = radius of the smaller base (m)
h = height of the frustum (m)
Description
What is this formula?
This formula calculates the volume of a frustum of a cone, which is the portion of a cone remaining after the top is cut off parallel to its base.
When to use it
Use this formula when calculating volumes of truncated conical shapes such as buckets, funnels, and engineering components.
Example
If a frustum has:
R = 5 m
r = 2 m
h = 6 m
V = (1/3)π(6)(25 + 10 + 4)
V = 3π(39)
V = 117π ≈ 367.57 m³
Applications
- Geometry and mathematics
- Engineering design
- Manufacturing
- Civil engineering structures
- Industrial containers
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