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Home > Solid of revolution

Assuming that the figure lies entirely on one side of the axis, the solid's volume is equal to the length of the circle described by the figure's barycenter, times the figure's area.

See also: surface of revolution

1 Formulas for solids of revolution

1.1 Rotations about the y-axis

The volume of the solid formed by rotating the area between the curves of and and the lines and about the y-axis is given by

If one of the bounding curves is actually the x-axis, then we can let in the formula above, and we have:

1.2 Rotations about the x-axis

The volume of the solid formed by rotating the area between the curves of and and the lines and about the x-axis is given by

As above, we can use

if one of the bounding curves is actually the x-axis.

2 External links

• Solid of Revolution at MathWorld
• Plot a solid of revolution

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Topics: Solid Of Revolution X''-axis Curves Figure Rotating Area Volume...

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