How does the Volume Of Revolution Calculator work?

Disk method: V = π ∫ [R(x)]² dx (rotate around x-axis) Then: Shell method: V = 2π ∫ x × f(x) dx Then: Washer method: V = π ∫ ([R(x)]² - [r(x)]²) dx Then: Fubini's theorem: switch methods if one difficult.

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

Example: Input y=x, 0-2, x-axis gives a result of V=8π/3.

Is the Volume 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 Volume Of Revolution Calculator?

Our Volume 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.

Mathematics

Volume Of Revolution Calculator

Volume of Revolution (Pappus)

Area of generating region

Distance traveled by centroid

Calculates volume when region rotates around axis creating 3D shape.

Symbol	Name	Unit	Description
V	π ∫ ([R(x)]² - [r(x)]²) dx	—	π ∫ ([R(x)]² - [r(x)]²) dx
R	R value	—	Variable used in the calculation

Difficulty:advanced

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Did You Know?

Volume of revolution elegantly shown: rotating f(x) around x-axis from 0 to 1 gives specific volume.

References

›Volume of Revolution

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Volume Of Revolution Calculator

Volume of Revolution (Pappus)

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Volume of Revolution (Pappus)