The cylinder is one of the basic conical shapes of geometry, and its properties have been known for thousands of years. In general, a cylinder is defined as the set of points that are a constant distance from a line segment, where the line segment is known as the axis of the cylinder.
In a broader sense, a cylinder can be defined as a curved surface formed by one line segment parallel to another line segment when moving in a path defined by a geometric equation. This definition enables several other cylinder types to be included in a cylinder family. If the cross section is an ellipse, the cylinder is an elliptical cylinder. If the cross section is a parabola or a hyperbola, it is called a parabolic or hyperbolic cylinder, respectively.
As a borderline case of the n-sided prisms one can imagine a circular cylinder in which n becomes infinite.
In general, the solid line described above serves as the axis of the cylinder, and each of the flat surfaces is called the base. The perpendicular distance between the bases is called the cylinder height.
Use the formula to find the volume of a cylinder
For a general cylinder with base area A and height h, the volume of the cylinder results from the formula:
V- cylinder = Ah
If the cylinder has a circular cross-section, the equation reduces to
V = πr 2 h
where r is the radius. Even if the shapes of the cylinders are not regular, ie the base of the cylinder does not form a right angle with the curved surface, the above equations apply.
In order to determine the volume of a cylinder, one should know two things:
- Height of the cylinder
- The cross-sectional area - if the cylinder has a circular cross-section, the radius must be known. In order to determine the elliptical or parabolic or hyperbolic area, other information is needed to determine the area and further calculations must be made.
Calculating the volume of a cylinder - examples
- The inner radius of a cylindrical water tank is 3 m. When the water is filled to a height of 1.5 m, determine the volume of water in the tank.
The radius of the base is given as 3m and the height as 1.5m. So if we apply the volume of a cylinder formula, we can get the volume of water in the tank.
V =? r 2 h = 3.14 × 3 × 2 = 1.5 3 42.39m
- A cylindrical fuel tank has a diameter of 6 m and a length of 20 m of fuel, the tank is only filled to 80% of its capacity. If a motor drains the tank in 1 hour and 40 minutes, find the average volume transfer rate of the pump.
In order to determine the volume flow of the pump, the total pumped volume must be determined. Therefore, it is necessary to calculate the volume of the tank. Since the diameter is given, we can determine the radius using the formula D = 2r. The radius is 3m. With the volume formula of a cylinder formula we have
V =? r 2 h = 3.14 × 3 × 2 = 20 565.2m 3
The fuel volume is only 80 of the total volume and it took 100 minutes to empty the tank, the volume flow is