Define the rotating region
- Select two different boundary graphs; one boundary may be the x-axis y = 0.
- Use a < b to define the part of the region that is rotated.
- Choose rotation around the x-axis or y-axis; the visualizer updates the orientation and base construction.
- If the selected boundaries coincide or create zero area, choose different graphs or a different interval.
Control the illustration
- Show or hide the middle cross-section, solid fill, between-graph fill, cross-section fill, base diameters and axis labels.
- Set separate colors for the uniform solid, the original plane region and the middle cross-section.
- Visible and hidden base arcs, radii, diameters and construction lines are drawn as editable vector objects.
- Use Line and Arrow to add explanatory construction marks; double-click them to change color, thickness or line style.
Volume and document output
- Draw solid of revolution creates the illustration without requiring a volume calculation.
- Calculate volume evaluates the selected region around the chosen axis and reports the result when it can be determined.
- Axes, text/formula annotations, local images and Undo/Redo remain available for the finished figure.
- SVG preserves vector lines and ellipses; PNG and Copy are convenient for Word and other documents.
Edit, save and export
- Use A to insert editable plain text or an Alpha Formula. Insert images from the device, and add Line or Arrow objects where those buttons are available.
- Select and drag objects directly. Double-click an object to edit it; image handles resize or rotate it, and Front/Back controls set its layer.
- Undo and Redo include drawing changes, object edits, table edits, inserted images and axis customizations.
- Save downloads a portable .ogp project containing Functions, Table, Shading, Revolution, Axes and their editable objects. HTML creates a launcher that restores the same saved scopes in a real OnlineGraphing.com tab.
- Open loads a saved .ogp project. PNG and Copy create raster output, while SVG remains vector-based and stays sharp when enlarged.
Use two boundaries that describe a genuine plane region on the selected interval. A zero-width or zero-area region cannot produce a visible solid.
Tip: save an .ogp project before making major changes so supported editable content can be restored later. The project file does not include Analysis results or entries from the Points tab.