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Gabriel's Horn is formed by rotating y = 1/x about the x-axis from x = 1 onward.
Its volume is V = π ∫₁^a (1/x)² dx = π(1 − 1/a), with limit π as a → ∞.
Its surface area obeys A = 2π ∫₁^a (1/x) √(1 + (1/x⁴)) dx > 2π ln(a), diverging to infinity as a → ∞.
The image renders this solid of revolution tapering along the axis labeled a.
It is used to demonstrate the painter's paradox of finite fill volume versus infinite coating area.