Since the values for the cylinder were already known, he obtained, for the first time, the corresponding values for the sphere.
The volume of a sphere of radius In some areas of geometry and topology the term cylinder refers to what we have called a cylindrical surface.
If such a plane contains two elements, it has a rectangle as a cylindric section, otherwise the sides of the cylindric section are portions of an ellipse.
In this article both points of view are presented and distinguished by referring to solid cylinders and cylindrical surfaces, but keep in mind that in the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the right circular cylinder.A cylindric section is the intersection of a cylinder's surface with a plane.They are, in general, curves and are special types of plane sections.First, consider planes that intersect a base in at most one point.A plane is tangent to the cylinder if it meets the cylinder in a single element.A right circular cylinder can also be thought of as the solid of revolution generated by rotating a rectangle about one of its sides.These cylinders are used in an integration technique (the "disk method") for obtaining volumes of solids of revolution.Indeed, one reason for the early emphasis (and sometimes exclusive treatment) on circular cylinders is that a circular base is the only type of geometric figure for which this technique works with the use of only elementary considerations (no appeal to calculus or more advanced mathematics).Terminology about prisms and cylinders is identical.These cases give rise to the hyperbolic, parabolic or elliptic cylinders respectively. The connection is very strong and many older texts treat prisms and cylinders simultaneously.Formulas for surface area and volume are derived from the corresponding formulas for prisms by using inscribed and circumscribed prisms and then letting the number of sides of the prism increase without bound.