Solids of Revolution
Use Tab to move through calculator controls. VoiceOver users can use the navigation shortcuts or Web Rotor to reach Calculator controls, the interactive graph, Graph description, or Selected slice details.
Graph description
Graph view controls
Applied region
Slice relationships
Integral construction
This constructs the volume integral; it does not evaluate the final volume.
Numerical details
Selected slice
Applied inputs
Input notation and controls
Enter an equation in the form shown by its field label. For example, y = sqrt(x) or x = y^2. Use sqrt(x), x^2, sin(x), arcsin(x), ln(x), pi, and e. Trigonometric angles are in radians. To select a branch, append constraints such as , x >= 0, y >= 0. A range such as , [0, inf) constrains the equation's input variable.
Enter a number or constant expression, such as sqrt(2) or pi/2. Leave either endpoint, or both, empty to calculate intersections automatically. Ambiguous regions may need an explicit bound or branch constraint.
Enter a horizontal line such as y = -1, or a vertical line such as x = 0.
Show slice controls the highlighted slice in the graph. Enable it before enabling Slice details. The text description and integral here are available independently.
VoiceOver: use Tab for buttons and fields. Press Control-Option-U to open the Web Rotor, then use its Links or Headings category to reach Calculator controls, the interactive graph, Graph description, or Selected slice details. Each displayed equation is announced as one complete formula. Use Control-Option-Right Arrow to continue reading.
On a focused graph: arrow keys orbit, Shift plus arrow keys pan, plus and minus zoom, and Home restores the view. Tab leaves the graph. The Graph view controls in Graph description provide equivalent buttons for pointer, Voice Control, and Switch Control users. On the slice preview, panning is disabled. Reset clears the revolution and slices but keeps the applied inputs.