Find truncated cone total and lateral surface area
Result
Frustum Surface Area
Step-by-Step Derivation
Frustum Surface Area Formula
A = π(R² + r² + (R + r)l)
Frustum surface area includes two circular ends and the curved side between them. The slant height is used for the lateral area, not the vertical height.
⚠Radii and slant height must be positive. Use slant height l for this surface area calculator.
How Frustum Surface Area Works
The curved side of a frustum unfolds into a ring sector. Adding the two base circles gives the total outside area.
Two Bases
The circular ends add πR² and πr².
Slant Height
l measures along the side.
Lateral Area
Curved area equals π(R+r)l.
Total Area
Base areas plus lateral area.
💡 Example: For R=6, r=3, and l=10, A=π(36+9+90)=424.115.
Applications of Frustum Surface Area
LampshadesFunnelsBucket CoversSheet Material
Frequently Asked Questions
What is a frustum surface area calculator?▼
It calculates the outside area of a truncated cone from two radii and slant height.
What is the frustum surface area formula?▼
The total area formula is A = π(R² + r² + (R+r)l).
How do I use this calculator?▼
Enter both radii and the slant height, then click Calculate.
What is frustum lateral area?▼
The lateral area is the curved side only, calculated as π(R+r)l.
Where is frustum surface area used?▼
It is used for tapered covers, lampshades, funnels, buckets, and sheet material estimates.
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