## cylinderx/a)^{2} + (y/b)^{2}
= 1. If a = b then the surface is a circular cylinder,
otherwise it is an elliptic cylinder. The cylinder is a degenerate quadric because at least one of the coordinates (in this case z) doesn't appear in
the equation, though by some definitions the cylinder isn't considered to
be a quadric at all. In common usage, a cylinder is taken to mean a finite
section of a right circular cylinder with its ends closed to form two circular
surfaces. If the cylinder has a radius r and a length h, then its volume
is V = πr ^{2}h and its surface area is
A = 2πr^{ 2} + 2πrh. For a given volume,
the cylinder with the smallest surface area has h = 2r. For
a given surface area, the cylinder with the largest volume has h
= 2r. More unusual types of cylinder include the imaginary
elliptic cylinder: (x/a)^{2} + (y/b)^{2}
= -1, the hyperbolic cylinder: (x/a)^{2}
- (y/b)^{2} = 1, and the parabolic cylinder:
x^{2} + 2y = 0.## Related category• SOLIDS AND SURFACES | ||||||

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