# Cylinder. Formulas and properties of a cylinder

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Definition of a cylinder
Elements of a cylinder
Right circular cylinder
Volume of a cylinder
Surface area of a cylinder
Oblique cylinder
Slanted cylinder

Definition.

**Cylinder**is a geometric body that limited cylindrical surface and two planes, called

**basics of cylinder**(top and bottom).

**A cylindrical surface**is a surface obtained by moving a straight line (generatrix) parallel to itself, along a flat curve.

**The cylinder bases**are plane figures formed by the intersection of a cylindrical surface with two planes.

Definition.

**Generatrix of cylinder**g is a combination of all segments parallel (AB), which connect the cylinder bases.Fig. 1 | Fig. 2 | Fig. 3 |

## Right circular cylinder

Commonly the word

**cylinder**is understood to refer to a finite section of a right circular cylinder having a finite height with circular ends perpendicular to the axis.Right circular cylinder described as a three-dimensional shape that is formed by rotating of rectangle on its side at 360°. In this case formed a right circular cylinder with a circle at the base of the cylinder.

Definition.

**Radius of cylinder**r of the cylinder is a radius of bases.Definition.

**Diameter of cylinder**d is a diameter of bases.Definition.

**Height of cylinder**h is a distance between the bases of the cylinder.Definition.

**Axis**is a line passing through the centers of the cylinder bases.Definition.

**Surface area**consisting of side area (lateral area), top area and bottom area.Definition.

**Axis section**is a section of the cylinder plane passing through the axis of the cylinder.Definition.

**Tangent plan**to the cylinder is a plane passing through the generatrix of the cylinder and perpendicular to the axial section of the cylinder.Formula.

where r is a radius of the base, h is height of a cylinder, d is diameter of the base.

**Volume of a cylinder**:V = πr^{2}h = π | d^{2} | h , |

4 |

Formula.

**Lateral area**(A_{l}) in terms of the radius and height:A_{l} = 2πrh = πdh

Formula.

**Surface area**(A_{s}) in terms of the radius and height:A_{s} = 2πr(h + r)

If the bases (top and bottom surfaces) are not parallel the cylinder called

**oblique**(Fig.2).If the foundations are not perpendicular to the height the cylinder called

**slanted**(Fig.3).
Geometry formulas
Square. Formulas and Properties of a Square
Rectangle. Formulas and Properties of a Rectangle
Parallelogram. Formulas and Properties of a Parallelogram
Rhombus. Formulas and Properties of a Rhombus
Circle, disk, segment, sector. Formulas and properties
Ellipse. Formulas and properties of ellipse
Cylinder. Formulas and properties of a cylinder
Cone. Formulas, characterizations and properties of a cone
Area. Formulas of area
Perimeter. Formulas of perimeter
Volume. Formulas of volume
Surface Area Formulas

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