# Cylinder Calculator

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Lets first understand, what is a cylinder and how we can find different properties of a cylinder?

Cylinder

A cylinder is a 3-D solid and one of the most basic of curvilinear geometric shapes. The cylinder is the idealized version of a solid physical tin can having lids on top and bottom.

Types of cylinder

A cylindrical surface is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. Any line in this family of parallel lines is called an element of the cylindrical surface.

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.

Right circular 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 the 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, the cylinder is called a circular cylinder. Generally we use 'cylinder' to refer a right circular cylinder.

The height of a cylinder is the perpendicular distance between its bases.

Cylinder of revolution

The cylinder obtained by rotating a line segment about a fixed line that it is parallel to is a cylinder of revolution. A cylinder of revolution is a right circular cylinder. The height of a cylinder of revolution is the length of the generating line segment. The line that the segment is revolved about is called the axis of the cylinder and it passes through the centers of the two bases.

Properties of cylinder

Sections of cylinder

A section of cylinder is the intersection of a cylinder's surface with a plane. The section of cylinder by a plane that contains two elements of a cylinder is a parallelogram. Such a cylindric section of a right cylinder is a rectangle.

A section of cylinder in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a right section of a cylinder. If a right section of a cylinder is a circle then the cylinder is a circular cylinder.

Generally, if a right section of a cylinder is a conic sections, parabola, ellipse, hyperbola, then the solid cylinder is called parabolic, elliptic and hyperbolic respectively.

Formulas

Let the Radius of the Cylinder be \(R\) units

and the Height of the Cylinder be \(H\) units.

Volume of cylinder

Volume of the Cylinder will be \(\pi R^2 H\) cubic units.

This formula holds whether or not the cylinder is a right cylinder.

Surface areas of cylinder

Area of the top base of the Cylinder: \(\pi R^2\)

Area of the bottom base of the Cylinder: \(\pi R^2\)

Area of the side of the Cylinder: \(2\pi RH\)

Total Surface Area of the Cylinder will be \(2\pi R(R + H)\) square units.

Curved Surface Area of the Cylinder will be \(2\pi R H\) square units.

For calculating different properties of the cylinder using above cylinder calculator, you have to just write the values in the given input boxes and press the calculate button, you will get the result.