103 LearnersLast updated on August 30, 2025
Surface Area of Open Cylinder
An open cylinder is a 3-dimensional shape with a circular base and a curved surface, but it does not have a top lid. The surface area of an open cylinder includes its curved surface and the base. In this article, we will learn about the surface area of an open cylinder.
What is the Surface Area of an Open Cylinder?
The surface area of an open cylinder is the total area occupied by the boundary or surface of the cylinder without the top lid. It is measured in square units.
An open cylinder has a circular base and a curved surface.
The surface area of an open cylinder includes the area of the curved surface and the base.
Surface Area of an Open Cylinder Formula
An open cylinder has two components for its surface area: the curved surface area and the base area. Look at the open cylinder below to see its surface area, height (h), and radius (r). An open cylinder has two types of surface areas: Curved Surface Area of an Open Cylinder Base Area of an Open Cylinder
Curved Surface Area of an Open Cylinder
The area of the curved part of the open cylinder is known as the curved surface area.
The formula for the CSA (Curved Surface Area) of the open cylinder is given as:
Curved Surface Area = 2πrh square units
Here, r is the radius of the base of the cylinder. h is the height of the cylinder.
Base Area of an Open Cylinder
The base area of an open cylinder is simply the area of the circular base. The formula for the base area is given as: Base Area = πr² square units Where r is the radius of the base of the cylinder.
Total Surface Area of an Open Cylinder
The total area occupied by the open cylinder, including the area of the curved surface and the area of the circular base, is known as the total surface area of an open cylinder.
The total surface area is calculated using the formula:
Total Surface Area = 2πrh + πr² square units Where r is the radius of the base, and h is the height of the cylinder.
Ignoring the Base Area
Students sometimes forget to include the base area while calculating the total surface area of an open cylinder. Always remember that the total surface area includes both the curved surface and the base.
Mistake 1
Using Diameter Instead of Radius
Some students mistakenly use the diameter instead of the radius in the formulas. Always ensure to use the radius, which is half of the diameter.
Mistake 2
Incorrect Value for π
A common mistake is using an incorrect value for π. Use either 3.14 or 22/7 for more accurate results.
Mistake 3
Confusing Height with Slant Height
In cylinders, only the vertical height is used, unlike cones that require slant height. Ensure to use the height (h) in calculations.
Mistake 4
Forgetting to Multiply by 2 for Curved Surface Area
When calculating the curved surface area, students often forget to multiply by 2. Remember, the formula is 2πrh, not just πrh.
Mistake 5
Solved Examples of Surface Area of Open Cylinder
Find the curved surface area of an open cylinder with a radius of 5 cm and height of 12 cm.
CSA = 376.8 cm²
Problem 1
Given r = 5 cm, h = 12 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 5 × 12 = 376.8 cm²
Find the total surface area of an open cylinder with a radius of 7 cm and height of 10 cm.
Explanation
TSA = 748.6 cm²
Problem 2
Use the formula: TSA = 2πrh + πr² = 2 × 3.14 × 7 × 10 + 3.14 × 7² = 439.6 + 153.86 = 593.46 cm²
An open cylinder has a radius of 3 cm and a height of 8 cm. Find the total surface area.
Explanation
TSA = 207.24 cm²
Problem 3
Use the formula: TSA = 2πrh + πr² = 2 × 3.14 × 3 × 8 + 3.14 × 3² = 150.72 + 28.26 = 178.98 cm²
Find the base area of an open cylinder with a radius of 4.5 cm.
Explanation
Base Area = 63.59 cm²
Problem 4
Base Area = πr² = 3.14 × 4.5² = 63.585 cm²
The curved surface area of an open cylinder is 200 cm², and its height is 5 cm. Find the radius.
Explanation
Radius = 6.37 cm
It is the total area that covers the outside of the cylinder, including its curved surface and the base.
1.What are the two types of surface area in an open cylinder?
2.What is the difference between height and slant height?
3.Is curved surface area the same as lateral surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of an Open Cylinder
Students often make mistakes while calculating the surface area of an open cylinder, which leads to incorrect answers. Below are some common mistakes and the ways to avoid them.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
