Cylinder Surface Area Calculator & Formula Analysis

Precision Note: Results rounded to 4 decimal places for educational reference.

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Historical Origins & Formula Derivation

The cylinder surface area formula has roots in ancient Greek geometry, with early developments by Archimedes who studied cylindrical shapes extensively. The modern formula combines the areas of two circular bases and the lateral surface area:

Formula: \( S = 2\pi r(r + h) \)

Where:
- \( r \) = base radius
- \( h \) = height of the cylinder
- \( \pi \) ≈ 3.1416 (mathematical constant)

Cylinder geometric diagram