Cone Surface Area Calculator
Calculate the surface area of a cone by entering the base radius and height. A cone has a circular base and curved surface meeting at a point.
🔺 Cone Surface Area
Formula
Cone Surface Area Formulas
Total Surface Area
Includes the circular base and the curved surface
Lateral Surface Area
Only the curved surface, excluding the base
Slant Height
Distance from apex to base edge along the surface
Volume
Volume of the cone
Cone Surface Area Examples
Example 1: Small Cone
Given: Radius = 3 cm, Height = 4 cm
Slant Height: l = √(3² + 4²) = √25 = 5 cm
Formula: SA = πr(r + l)
Solution: SA = π × 3 × (3 + 5) = 3π × 8 = 24π ≈ 75.40 cm²
Example 2: Medium Cone
Given: Radius = 5 cm, Height = 12 cm
Slant Height: l = √(5² + 12²) = √169 = 13 cm
Formula: SA = πr(r + l)
Solution: SA = π × 5 × (5 + 13) = 5π × 18 = 90π ≈ 282.74 cm²
Example 3: Large Cone
Given: Radius = 8 cm, Height = 15 cm
Slant Height: l = √(8² + 15²) = √289 = 17 cm
Formula: SA = πr(r + l)
Solution: SA = π × 8 × (8 + 17) = 8π × 25 = 200π ≈ 628.32 cm²
Cone Surface Area FAQ
What is a cone?
A cone is a 3D shape with a circular base and a curved surface that tapers to a single point (apex). Common examples include ice cream cones and traffic cones.
What is slant height?
Slant height is the distance from the apex to any point on the base circumference, measured along the cone's surface. It's calculated as l = √(r² + h²).
What's the difference between height and slant height?
Height (h) is the vertical distance from base to apex. Slant height (l) is the distance along the cone's surface from apex to base edge.
How do you calculate cone surface area?
Total surface area uses SA = πr(r + l), which includes the base and curved surface. Lateral surface area uses LSA = πrl for just the curved part.