Total Surface Area of a Cone
Total Surface Area of a Cone
\[A = \pi r(r + l)\]
Variables
A = total surface area (m²)
r = radius of the cone base (m)
l = slant height of the cone (m)
Description
What is this formula?
This formula calculates the total surface area of a cone, including both the circular base and the curved lateral surface.
When to use it
Use this formula when determining the complete external area of conical objects or structures.
Example
If a cone has:
radius = 3 m
slant height = 5 m
A = π × 3 × (3 + 5)
A = 24π
A ≈ 75.40 m²
Applications
- Geometry and mathematics
- Engineering calculations
- Industrial manufacturing
- Surface coating estimation
- Architecture and design
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