Before getting to the main formula that is used to calculate the volume of cylinder, let’s learn more information about this geometrical figure, its elements, properties, and sections.
There are many objects around us that are physical models of the cylinder. For example, many machine parts have a cylindrical shape or represent a combination thereof, and majestic columns of churches and cathedrals are also made in the shape of cylinders, which emphasizes their beauty and harmony.
Euclid thought of a cylinder as a figure that can be obtained by rotating the rectangle. So, cylinder is a geometric body bounded by a cylindrical surface and two parallel planes that intersect it. The formula for finding the volume of cylinder has been known in the Ancient Greece, where it was formed.
A cylindrical surface is the surface, obtained in such a reciprocating movement of a straight line (generator) in the space that the point of the generator moves along a flat curve (directrix). The part of the surface of the cylinder that is bounded by a cylindrical surface called the cylinder surface. Another part bounded by parallel planes is the base of the cylinder. Thus, the border of the base will be of the same shape as the directrix.
In most cases, a cylinder is understood as a right circular cylinder, where the directrix – the circle and the base is perpendicular to the generator. Such a cylinder has an axis of symmetry.
Other cylinder types (by the slope of the generator) can be oblique or sloping (if the generator doesn’t touch the base at right angles). Due to the shape of the base, cylinders can be elliptical, hyperbolic, and parabolic.
Prism is also a kind of the cylinder with a base in the form of a polygon.
Another definition for a cylinder is that it is the body, which is formed by the rotation of a rectangle around the line, including its side.
Circles are called bases of the cylinder, and the segments joining the corresponding points of the circles are the generatrixes of a cylinder.
Since parallel transportation is a movement, the bases of the cylinder are equal.
Since during the parallel transformation a plane moves parallel to the plane (or in itself), the bases of the cylinder lie in parallel planes.
Since during the parallel transformation the points are shifted by parallel (or matched) lines on the same distance, the generatrixes of the cylinder are parallel and equal.
The surface of a cylinder consists of bases and the side surface. The side surface is made up of generators.
The cylinder is direct if its generators are perpendicular to the plane of the bases.
Visually, a direct cylinder can be represented as a geometric body that describes a rectangle while rotating around its side.
The radius of the cylinder is the radius of its base. Cylinder’s altitude represents the distance between the planes of its bases. Cylinder’s axis represents a straight that goes through the center of the base. This line is parallel to the generating lines.
Cylinder is equilateral if its height is equal to the diameter of the base.
If the bases of the cylinder are plane (and therefore the planes containing them are parallel), then this is a cylinder standing on a plane. If the bases of the cylinder standing on a plane are perpendicular to the generating line, the cylinder is direct.
In particular, if the base of the cylinder standing on the plane is circle, then this cylinder is circular. If in the base of the cylinder is ellipse, then this is the elliptical cylinder.
The section of the cylinder with a plan, which is parallel to the axis, is a rectangle. Two sides of this rectangle form a cylinder, while the other two sides are parallel chords to the bases.
In particular, the axial section is a rectangle. This is the section of the cylinder with the plane that passes through its axis.
The section of a cylinder with plane parallel to the ground is circle.
The section of a cylinder with a plane that is not parallel to the base and the axis is oval.
Finding the Volume of Cylinder
If you have a value of a diameter, divide it by 2 to get the radius.
If you have a circumference, divide it by 2 pi to get the radius.
Advice for Finding the Volume of Cylinder
Formulas for Calculating the Volume of Cylinder of Various Kinds
There are two formulas that can help you find the volume of cylinder that is inclined:
For direct cylinder, h = l.
For direct cylinder, sin f = 1, l = h and S = S, so the volume of cylinder is equal to V = Sl = Sh.
For a circular cylinder, the formula for the volume of cylinder is V = pi R2h = pi x d2/4 x h, where d is the diameter of the base.
Many objects that surround us are cylinders. Pots, jars for bulk products, lamps, vases, bottles, cans, cars, details, and crayons are all represent cylinders in one or another of their form. It is very important to know the formula of volume of cylinder in order to be able to build various details, buildings, and other objects of the right size. The volume of cylinder formula is considered to be one of the simplest in geometry.