Surface Area of a Cone Formula
What is the formula for the surface area of a cone?
Answer
Here r is the radius, l is the slant height of a face, or the length along the solid. The result comes out in square units.
Where the formula comes from
Cut the cone up one side and flatten it: the curved part opens into a sector of a circle of radius l, and its area works out to πrl. Add the base disc πr². If you know the height instead of the slant, l = √(r² + h²). Both steps assume a RIGHT circular cone — on a leaning one the slant is a different length on every side and neither formula holds.
Worked examples
Let r = 3, l = 5. Then the surface area of a cone ≈ 75.4 square units.
Let r = 2.5, l = 6.5. Then the surface area of a cone ≈ 70.69 square units.
The common mistake
Putting the height h in place of the slant l. Of the two, h is always the shorter — they are linked by l² = r² + h². The pyramid's surface area asks for a slant too, but a different one: the slant height of a triangular FACE, not of the whole solid.
Other quantities: Cone
Related Calculations
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
<a href="https://calculat.io/en/geometry/shape-formula/surface-area--cone">Surface Area of a Cone Formula - Calculatio</a>
Values from the Formula (l = 5)
| If r = | Surface area |
|---|---|
| 1 | ≈ 18.85 square units |
| 2 | ≈ 43.98 square units |
| 3 | ≈ 75.4 square units |
| 3.5 | ≈ 93.46 square units |
| 4 | ≈ 113.1 square units |
| 4.5 | ≈ 134.3 square units |