Solids of Revolution
Solids of Revolution projects an interactive 3D mesh and shows disk, washer or shell volume estimates locally in your browser.
Full-solid estimate
Exact full volume
Absolute error
Drag to orbit. The surface is a projected 3D mesh; transparency reveals the selected slice.
Representative slice ΔV
Slice width
At a glance
- Accepts
- Four preset regions, revolution angle, slice coordinate, 4–120 subdivisions, camera controls
- Outputs
- Projected 3D solid, original region, representative slice and full-solid volume comparison
- Where it runs
- Entirely in your browser, on your device
- What leaves your device
- No calculation inputs are uploaded; standard site usage analytics still apply
- Limits
- Preset regions and axes only; orthographic SVG mesh; volume metrics refer to full 360-degree solids
- Account
- Not required - there is no sign-up
- Price
- Free, with no watermark and no usage cap
- Made by
- Visrut
- Last updated
- 14 October 2026
What to notice
Disks and washers slice perpendicular to the rotation axis: volume is π∫(R² − r²) dx. Shells slice parallel to it: volume is 2π∫radius × height dr.
The gold surface marks one representative slice at the selected coordinate. Its displayed contribution uses the subdivision width. The estimate sums midpoint samples over the entire region; the exact volume comes from the preset’s integral.
The shell example rotates a 2-by-2 rectangle about the y-axis into a cylinder. The other examples rotate about the x-axis. Revolution angle changes the picture, while the volume metrics refer to the complete 360° solid.
Reference: disks and washersReference: cylindrical shells
Frequently asked questions
Are these symbolic calculators?
These tools teach through supported function presets, exact derivatives and antiderivatives where supplied, and labelled numerical approximations. They do not evaluate arbitrary expressions.
Do calculations leave my device?
All graphs and calculations run locally in your browser. No account or external calculation service is required.