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Surface of revolution illustration

The surface of revolution formed by rotating around the y-axis.

A Solid of revolution is a solid formed by the rotation of a function around a line. Many common shapes, such as spheres, cones, and cylinders are solids of revolution. The volume of such a solid can be calculated by using rings or shells, or by using a double integral in the form

assuming the rotation is about the line .

The surface of revolution is the surface enclosing the solid. The surface area of a surface of revolution can be found with the formula

Examples[]

Find the volume of the solid of revolution obtained when the function

(a semicircle rotated to obtain a sphere) is rotated about the -axis.


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