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   Cylinder Formulas   

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also see Defining Geometric Figures

A cylinder is a surface generated by a family of all lines parallel to a given line (the generatrix) and passing through a curve in a plane (the directrix). A right section is the curve formed by the intersection of the surface and a plane perpendicular to the generatrix. The parallel bases of a cylinder may form any angle with the axis.

More commonly, a cylinder includes the solid enclosed by a cylinder and two parallel planes. The region of either of the parallel planes enclosed by the surface is called a base of the cylinder. The perpendicular distance between the planes of the bases is the height of the cylinder. The line segment cut on any of the generating lines by the two parallel planes is called a lateral edge.


 Circular Cylinder

    A cylinder whose bases are circles. The line connecting the centers of the bases
    is called the axis.

 
     Height: h
     Area of base: B
     Length of lateral edge: l
     Area of right section: A
     Perimeter of right section: P

     Lateral surface area: S
     Total surface area: T
     Volume: V

          S = lP
          T = lP + 2B
          V = hB = lA


 



 Right Circular Cylinder

     A circular cylinder in which the axis is perpendicular to the bases. (If the axis
     of a circular cylinder is not perpendicular to the bases, it is called an oblique
     circular cylinder.)


     Height: h
     Radius of base: r
     Lateral surface area: S
     Total surface area: T
     Volume: V

          S = 2 Pi rh
          T = 2 Pi r(r+h)
          V = Pi r2h
          A = B = Pi r2
          P = 2 Pi r
          l = h

 

For more about cylinders, visit:

Ask Dr. Math: Surface Area and Volume of Cylinders
The Geometry Center: Cylinders

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