Cylinder Volume Formula

V = π × r² × h, plus surface area and lateral area

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

A cylinder is a 3D shape with two parallel circular faces (bases) connected by a curved surface. Its volume is simply the base area (πr²) multiplied by the height — making cylinder formulas some of the easiest in 3D geometry.

The Formulas

Name Formula Notes
Volume V = π × r² × h r = radius of the base, h = height between the bases.
Total Surface Area SA = 2πr² + 2πrh Two circular bases + lateral curved area.
Lateral Surface Area LSA = 2π × r × h Just the curved side, no top or bottom.
Base Area A_base = π × r² Each circular cap.
Hollow Cylinder Volume V = π × (R² − r²) × h R = outer radius, r = inner radius (pipes, tubes).

Worked Examples

Example 1: A cylinder with radius 3 cm and height 10 cm

  1. V = π × 3² × 10 = 90π ≈ 282.74 cm³
  2. SA = 2π × 3² + 2π × 3 × 10 = 18π + 60π = 78π ≈ 245.04 cm²

Example 2: Find the height when V = 500 cm³ and r = 5 cm

  1. V = πr²h → h = V/(πr²) = 500/(π × 25)
  2. h = 500/(25π) ≈ 6.37 cm

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