Find cone total surface area from radius and slant height
Result
Cone Surface Area
Step-by-Step Derivation
Cone Surface Area Formula
A = πr(r + l)
Cone surface area includes the circular base and the curved side. The slant height measures the side length from base edge to apex and is required for the lateral area.
⚠Slant height must be at least as large as the radius. Use vertical height only for volume, not for this surface area formula.
How Cone Surface Area Works
The curved side of a cone unfolds into a sector. Its area is πrl, and adding the base area πr² gives total surface area.
Radius
Distance from base center to edge.
Slant Height
Side distance from edge to apex.
Lateral Area
Curved side area equals πrl.
Total Area
Base plus lateral area.
💡 Example: For r=4 and l=9, A=π(4)(4+9)=163.363 square units.
Applications of Cone Surface Area
FunnelsCone CoversCraft TemplatesManufacturing
Frequently Asked Questions
What is a cone surface area calculator?▼
It calculates the outside area of a cone from radius and slant height.
What is the cone surface area formula?▼
The total surface area formula is A = πr(r+l), where l is slant height.
How do I use this calculator?▼
Enter radius and slant height, then click Calculate to get total area, lateral area, and vertical height.
What is lateral area of a cone?▼
Lateral area is the curved side only, calculated as πrl.
Where is cone surface area used?▼
It is used for funnels, cone covers, crafts, roof shapes, manufacturing, and geometry homework.
Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.