Information about Cylinder (geometry)
In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates:
This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). Even more general is the generalized cylinder: the cross-section can be any curve.
The cylinder is a degenerate quadric because at least one of the coordinates (in this case z) does not appear in the equation. By some definitions the cylinder is not 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, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by
and its surface area is:
With the top and bottom, the surface area is
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, i.e. the cylinder fits in a cube (height = diameter.)
There are other more unusual types of cylinders. These are the imaginary elliptic cylinders:
the hyperbolic cylinder:
and the parabolic cylinder:
In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface defined as the locus of zeros of a quadratic polynomial.
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In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface defined as the locus of zeros of a quadratic polynomial.
..... Click the link for more information.
This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). Even more general is the generalized cylinder: the cross-section can be any curve.
The cylinder is a degenerate quadric because at least one of the coordinates (in this case z) does not appear in the equation. By some definitions the cylinder is not 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, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by
and its surface area is:
- Area of the top is
- Area of the bottom is
- Area of the side is
With the top and bottom, the surface area is
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, i.e. the cylinder fits in a cube (height = diameter.)
There are other more unusual types of cylinders. These are the imaginary elliptic cylinders:
the hyperbolic cylinder:
and the parabolic cylinder:
See also
- Steinmetz solid, the intersection of two or three perpendicular cylinders
- Prism (geometry)
External links
- Surface Area MATHguide
- Volume MATHguide
- Spinning Cylinder Math Is Fun
- calculate surface area and volume with your own values
- Paper model cylinder
Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface defined as the locus of zeros of a quadratic polynomial.
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Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane through two numbers, usually called the x-coordinate and the y-coordinate of the point.
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In geometry, a cross section is the intersection of a body in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross sections.
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For the computing company, see .
In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface defined as the locus of zeros of a quadratic polynomial.
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In classical geometry, a radius (plural: radii) of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment. The radius is half the diameter.
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The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
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Area is the measure of how much exposed area any two dimensional object has. It is expressed in square units, and is calculated by adding together the areas of all the faces of the object.
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Area formulas
Note: For 2D figures, the surface area and the area are the same...... Click the link for more information.
In geometry, the Steinmetz solid is the solid body generated by the intersection of two or three cylinders of equal radius at right angles. It is named after Charles Proteus Steinmetz, though these solids were known long before Steinmetz studied them.
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prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same. A prism is a subclass of the prismatoids.
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