How does the Surface Of Revolution Calculator work?

S = 2π ∫ r(t) × √((dx/dt)² + (dy/dt)²) dt (parametric) Then: S = 2π ∫ y × √(1 + (dy/dx)²) dx (Cartesian, rotate around x-axis) Then: r(t) = distance to axis; integrand = arc length element Then: Accounts for both stretching and distance from axis.

Can you give an example of how to use the Surface Of Revolution Calculator?

Example: Input y=x, 0 to 2, x-axis gives a result of SA=4π*sqrt(2).

Is the Surface Of Revolution Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Surface Of Revolution Calculator?

Our Surface Of Revolution Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Surface Of Revolution Calculator

Surface of Revolution (Pappus)

Radius of generating curve (r)

Distance traveled by centroid (d)

Calculates surface area when curve rotates around axis creating 3D shape.

Symbol	Name	Unit	Description
S	2π ∫ y × √(1 + (dy/dx)²) dx (Cartesian	—	2π ∫ y × √(1 + (dy/dx)²) dx (Cartesian

Difficulty:advanced

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Did You Know?

Surface of revolution derived from Pappus's theorem: S = arc length × circumference of path.

References

›Surface of Revolution Calculator

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Surface Of Revolution Calculator

Surface of Revolution (Pappus)

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Surface of Revolution (Pappus)