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The surface area of Revolution can be obtained if a curve is rotated on an axis. There are two cases that revolve around; x and y-axis. The formulas used for finding out the surface area of revolutionaries depend on the axis of rotation and the original function.

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Surface Area of Revolution

A surface of Revolution is a 3D surface that has circular cross-sections such as a bell, vase, or a wine bottle. In these problems, you need to divide a surface into circular bands, find out the surface area of a band and then add up the band areas to get a total surface area.

The examples of the surface area of revolution that are generated by straight lines are conical and cylindrical surfaces and they depend on whether a line is parallel to an axis or not.


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Circles that are rotated around a diameter give a sphere, which is a great circle. If a circle rotates around an axis, which does not intersect the inside of a circle then it gives a torus that does not intersect a ring torus.

The properties of Surface Area of Revolution

The sections of a surface area of revolution that is made by planes through an axis are known as meridional sections. A meridional section is considered as a generatrix in a plane decided by the axis. The surface of the revolution that is made by planes perpendicular to an axis is known as circles. There are some special cases of elliptic paraboloids and hyperboloids that are surfaces of revolution. They are identified as quadratic surfaces and they are cross-sections and perpendicular to an axis.

A surface of revolution that features a hole in it, wherein an axis of revolution would not intersect a surface, is understood as a toroid. If a rectangle is rotated around the axis that is parallel to one of the edges then it produces a hollow ring-like section. When a revolved figure is a circle then an object is known as a tourist. The properties are discussed in our Assignment help online of Surface Area of Revolution.

What Are The Applications Of the Surface Area Of Revolution?

This concept is used for finding out an arc length of curves that can be extended for finding out the surface area of a revolution. The surface area of Revolution has uses in multiple fields of study. It has applications in the fields of engineering and physics. If a certain object is digitally designed then the revolution can be used for deciding the surface area without measuring the radios and length of an object that is being designed. The applications are discussed in detail in our Surface Area of Revolution Assignment Help.


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