Cone Surface Area Formula

Total + lateral surface area, with slant height

Reviewed by [email protected], Geometry Calculator Developer & Online Math Educator Last updated May 8, 2026

A cone's surface area is the sum of the circular base (πr²) and the lateral curved surface (πrl), where l is the slant height — not the vertical height. The slant height connects the rim of the base to the apex along the surface.

The Formulas

Name Formula Notes
Total Surface Area SA = πr² + πrl = πr(r + l) Base + curved side.
Lateral Surface Area LSA = π × r × l Just the curved side, used when wrapping a cone.
Slant Height l = √(r² + h²) r = base radius, h = vertical (perpendicular) height.
Volume V = ⅓ × π × r² × h Exactly 1/3 of the cylinder with same base + height.
Base Circumference C = 2π × r Equal to the arc length of the unrolled lateral surface.

Worked Examples

Example 1: A cone with radius 4 cm and height 3 cm

  1. Slant height: l = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
  2. Lateral SA: LSA = π × 4 × 5 = 20π ≈ 62.83 cm²
  3. Total SA: SA = π × 4² + 20π = 16π + 20π = 36π ≈ 113.10 cm²

Example 2: Find the slant height when r = 6 and total SA = 90π

  1. SA = πr² + πrl → 90π = 36π + 6πl
  2. 54π = 6πl → l = 9 cm

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