Geometry · March 25, 2026
What Is a Cylinder? Definition, Properties, and Real-Life Examples
A cylinder is a three-dimensional solid figure with two identical circular bases joined by a curved surface. This guide covers the cylinder definition, 4 types, 5 properties, all cylinder formulas, the net of a cylinder, and real-world examples of cylindrical objects.
What Is a Cylinder?
A cylinder is a three-dimensional (3D) solid figure that has two identical circular bases joined by a curved surface at a particular distance from the center. The distance between the two circular bases is the height of the cylinder. Toilet paper rolls, cold drink cans, and soup cans are real-life examples of cylinders. The Leaning Tower of Pisa is cylindrical in shape.
The word "cylinder" comes from the Greek word "kylindros," meaning "roll" or "roller." In mathematics, a cylinder is a geometric shape with a circular base and straight sides. The term applies to cylindrical objects such as pipes, containers, and engine parts.
A cylinder has 2 circular bases + 1 curved surface. Hover to highlight parts.
Cylinder Definition
A cylinder is a 3D solid shape that consists of two identical and parallel circular bases linked by a curved surface. These bases are circular disks. The line passing from the center or joining the centers of two circular bases is called the axis of the cylinder shape. The perpendicular distance between the two bases is the height, represented as "h." The distance from the center to the outer boundary of the circular base is the radius of the cylinder, represented by "r." A cylinder is a combination of 2 circles + 1 rectangle.
Real-life examples of the cylinder shape include pipes, fire extinguishers, water tanks, and cold-drink cans.
Cylinder Faces Vertices Edges
A cylinder has two circular faces and one curved surface. The two circular faces are congruent (equal in size and shape) and are located at each end of the cylinder. The curved surface connects the two circular faces and is shaped like a rectangle rolled into a tube.
- Faces: A cylinder has 3 faces in total (2 flat circular faces + 1 curved face)
- Edges: A cylinder has 2 curved edges (one at the top and one at the bottom)
- Vertices: A cylinder has 0 vertices (the two edges never meet at a point)
Click each card to highlight the corresponding part on a cylinder. Unlike a cone, cube, or cuboid, a cylinder has no vertex.
Types of Cylinder
There are 4 different types of cylinders in geometry.
Right Circular Cylinder
A right circular cylinder has an axis perpendicular to the center of the base. The two parallel circular bases are directly above each other. Example: a soda can.
Right circular cylinder: axis is perpendicular to both circular bases. V = πr²h
Oblique Cylinder
An oblique cylinder has sides that lean over the base. The sides are not perpendicular to the center of the base. Example: the Leaning Tower of Pisa.
Oblique cylinder: the axis tilts at an angle. Volume still equals πr²h (perpendicular height).
Elliptic Cylinder
An elliptic cylinder has bases in the form of an ellipse instead of a circle. Example: an optical lens.
Elliptic cylinder: base is an ellipse. V = π × a × b × h
Right Circular Hollow Cylinder or Cylindrical Shell
A right circular hollow cylinder (cylindrical shell) consists of two right circular cylinders bounded one inside the other. The axis is common and perpendicular to the central base. A hollow cylinder has a void or space inside. Example: hydraulic cylinders.
Hollow cylinder: V = π × h × (R² − r²), where R = outer radius, r = inner radius.
Properties of Cylinder
A cylinder shape has 5 properties that separate a cylinder from other geometric figures:
- A cylinder has one curved surface and two flat faces that are identical.
- The two circular bases are congruent to each other.
- The size of a cylinder depends on the radius of the base and the height of the curved surface.
- A cylinder has no vertex. Unlike a cone, cube, or cuboid, there is no corner present in the cylinder.
- The base and the top of the cylinder are identical — either circular or elliptical.
Cylinder compared to other 3D geometric figures:
Cylinder
0 vertices
Cone
1 vertex
Cube
8 vertices
Sphere
0 vertices
Formulas of Cylinder
Every three-dimensional geometric figure has a minimum of 2 major formulas: surface area and volume. A cylinder has 3 major formulas related to surface areas and volume:
- Lateral Surface Area (LSA) or Curved Surface Area (CSA) of cylinder = 2πrh
- Total Surface Area (TSA) of cylinder = 2πr(h+r)
- Volume of cylinder = πr²h
In all 3 formulas, "r" represents the base radius and "h" represents the height of the cylinder.
Curved Surface Area of Cylinder
The Curved Surface Area (CSA) is the area formed by the curved surface of the cylinder — the space between the two parallel circular bases. The CSA formula is:
The value of π is 22/7 or approximately 3.14. When the curved face of a cylinder is unfolded, the result is a rectangle whose length = circumference of the circle = 2πr and width = height of the cylinder = h. The area of this rectangle: length × width = 2πr × h.
Total Surface Area of Cylinder
The Total Surface Area (TSA) of a cylinder defines the total area the cylinder occupies including the bases. A cylinder consists of two circles and one curved sheet. To find the TSA, add the curved surface area and the area of two circles:
CSA = 2πrh | Area of a Circle = πr²
There are two circles in a cylinder, so multiply the area of the base circle by 2.
Volume of Cylinder
The volume of a cylinder defines the density or amount of space the cylinder occupies. To fill a cylinder with water, the amount of water needed can be calculated by finding the cylinder volume.
Volume of a cylinder = Area of a circle × height
Try the Cylinder Volume Calculator
Calculate cylinder volume, curved surface area, and total surface area instantly with our free online tool.
🧮 Open Cylinder Volume CalculatorRelated Cylinder Calculators:
Net of a Cylinder
The net of a cylinder is a 2D structure made by unfolding the 3D cylinder shape. A cylinder net helps visualize the shape of a cylinder and the surface area calculation. When a cylinder is unfolded, the result is a rectangle joined by two identical circles that form the top and bottom bases.
The rectangle width = height (h), and the rectangle length = circumference of the circle (2πr). The two circles each have area πr².
Net of a cylinder: two identical circles (bases) and one rectangle (curved surface unrolled).
Real-World Examples
Cylindrical shapes appear everywhere in daily life. There are 8 common real-life examples of cylinders:
- Toilet paper rolls — hollow cylindrical shells used in households worldwide
- Cold drink cans — right circular cylinders made of aluminum, holding 355 ml (12 fl oz) of liquid
- Pipes — hollow cylinders used in plumbing, construction, and industrial engineering
- Fire extinguishers — pressurized cylindrical containers for fire safety
- Water tanks — large cylindrical storage containers holding thousands of liters (gallons) of water
- Soup cans — common right circular cylinders found in kitchens
- Beakers — cylindrical glass containers used in chemistry laboratories
- Leaning Tower of Pisa — an oblique cylinder, 56 meters (183.7 feet) tall with an 8-story structure
List All Formulas of Cylinder
All formulas related to a cylinder of radius "r" and height "h":
| Formula Name | Expression | Unit |
|---|---|---|
| Base Area | πr² | square units |
| Curved Surface Area (CSA) | 2πrh | square units |
| Total Surface Area (TSA) | 2πr(h+r) | square units |
| Volume | πr²h | cubic units |
Use the Cylinder Volume Calculator to calculate cylinder volume instantly. Use the Cylinder Geometry Calculator to find any missing cylinder dimension.
FAQs on Cylinder Shape
What is a Cylinder?
A cylinder is a 3D solid shape with two identical circular bases connected by a curved surface. A cylinder has 3 faces, 2 edges, and 0 vertices.
What are the Cylinder Formulas?
The 3 major cylinder formulas are: Curved Surface Area (CSA) = 2πrh square units, Total Surface Area (TSA) = 2πr(h+r) square units, and Volume = πr²h cubic units.
What is the Surface Area of a Cylinder?
The surface area of a cylinder has 2 types: Curved Surface Area (CSA) = 2πrh square units, and Total Surface Area (TSA) = 2πr(h+r) square units, where r is the radius and h is the height of the cylinder.
What is the Volume of a Cylinder?
The volume of a cylinder is the space occupied by the cylinder. The volume formula is V = πr²h cubic units, where r is the base radius and h is the height.
How Many Edges Does a Cylinder Have?
A cylinder has 2 curved edges. One edge is at the top and one at the bottom where the flat circular faces meet the curved surface.
What are the Real-Life Cylinder Examples?
Real-life cylinder examples include toilet paper rolls, cold drink cans, pipes, fire extinguishers, water tanks, soup cans, beakers, and torches.
What is the Base Area of the Cylinder?
The base area of the cylinder is the area within the circular base, calculated using πr² where r is the radius. Base area is measured in square units such as square centimeters (cm²), square inches (in²), or square feet (ft²).
What is a Total Surface Area of Cylinder?
The Total Surface Area (TSA) of a cylinder equals the sum of the curved surface area and the area of the two circular bases: TSA = 2πrh + 2πr² = 2πr(h+r) square units.
What are the Properties of a Cylinder?
A cylinder has 5 key properties: one curved surface and two identical flat circular faces, two congruent circular bases, size depends on radius and height, no vertex or corner, and identical top and bottom bases.
How Many Faces Does a Cylinder Have?
A cylinder has 3 faces in total: 2 flat circular faces (top and bottom) and 1 curved face connecting the two circular faces.
Is Euler's Formula Applicable for Cylinder?
No, Euler's formula is not applicable for a cylinder. Euler's formula applies only to polyhedra (3D shapes with flat faces only). A cylinder has a curved surface, so Euler's formula does not apply.
What is cylinder in mathematics?
In mathematics, a cylinder is a geometric solid with a constant circular cross-section. A cylinder consists of two parallel, congruent circular bases joined by a curved surface at a fixed distance (height) from the center.
What is a cylinder for kids?
A cylinder is a 3D shape that looks like a tube or a can. A cylinder has a circle on the top, a circle on the bottom, and a curved surface wrapped around the two circles. Soup cans, toilet paper rolls, and drinking glasses are all cylinder shapes.