Cylinder
Cylinder
This traditional view is still used in elementary treatments of geometry, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface and this is how a cylinder is now defined in various modern branches of geometry and topology.
Video: Cylinders: Lesson (Basic Geometry Concepts)
A solid bounded by a cylindrical surface and two parallel planes is called a (solid) cylinder. The line segments determined by an element of the cylindrical surface between the two parallel planes is called an element of the cylinder. All the elements of a cylinder have equal lengths. The region bounded by the cylindrical surface in either of the parallel planes is called a base of the cylinder. The two bases of a cylinder are congruent figures. If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder, otherwise it is called an oblique cylinder. If the bases are disks (regions whose boundary is a circle) the cylinder is called a circular cylinder. In some elementary treatments, a cylinder always means a circular cylinder.
Right circular cylinders
Video: What is a Right Circular Cone?
The bare term cylinder often refers to a solid cylinder with circular ends perpendicular to the axis, that is, a right circular cylinder, as shown in the figure. The cylindrical surface without the ends is called an open cylinder.
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.
Cylindric sections
Cylindric section
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. The cylindric section by a plane that contains two elements of a cylinder is a parallelogram. Such a cylindric section of a right cylinder is a rectangle.
Video: Cylindrical sections
A cylindric section in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a right section. If a right section of a cylinder is a circle then the cylinder is a circular cylinder. In more generality, if a right section of a cylinder is a conic section (parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic or hyperbolic respectively.
Volume
Video: Volume Of A Cylinder
If the base of a circular cylinder has a radius r and the cylinder has height h, then its volume is given by
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V = πr2h.
This formula holds whether or not the cylinder is a right cylinder.
Surface area
Video: Surface Area of a Cylinder
Having radius r and altitude (height) h, the surface area of a ......
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