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Surface Area of Revolution
A surface of revolution is a 3D surface having circular cross-sections just like a bell or a vase or a bottle of liquid. For such problems, it is important to split the surface into contracted circular bands. This allows you to figure out the surface area of a depicted band and then obtain the total surface area by summing up the surface areas of all the bands.
A surface of revolution is basically a surface that is created in Euclidean space by rotating a curve or the generatrix surrounding an axis of rotation. The examples of surfaces of revolution that are generated by a straight line include conical and cylindrical surfaces based on whether the line remains parallel to the axis or not. A sphere is generated of which a great circle is produced by rotating a circle around a diameter. And a torus is generated, which is a ring torus that does not intersect itself by rotating the circle around an axis not intersecting the inner of a circle.
The surface of revolution consists of the sections that are made by planes using the axis called meridional sections. It is possible to consider a meridional section as the generatrix in the plane found out using the same and the axis. A few special cases of elliptic paraboloids and hyperboloids of either a single or multiple sheets fall under surfaces of revolution. It is possible to identify these as quadratic surfaces whose cross sections that are perpendicular to the axis are circular.
The application of surfaces of revolution is necessary for numerous fields in engineering and physics. It is possible to use certain digitally designed objects to find out the surface area without using the measurements of the radius and length of the object in use.
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