102 LearnersLast updated on August 30, 2025
Surface Area of Circular Cylinder
A cylinder is a 3-dimensional shape with two parallel circular bases connected by a curved surface. The surface area of a cylinder is the total area covered by its outer surface. The surface area of the cylinder includes both its curved surface and the bases. In this article, we will learn about the surface area of a circular cylinder.
What is the Surface Area of a Circular Cylinder?
The surface area of a cylinder is the total area occupied by the boundary or surface of a cylinder.
It is measured in square units.
A cylinder is a 3D shape with two parallel circular bases and a curved side that connects the bases.
Cylinders are classified into two types: right circular cylinders and oblique cylinders.
When the axis of the cylinder is perpendicular to the bases, it forms a neat, even shape called a right circular cylinder.
If the axis is not perpendicular to the bases and the cylinder leans to one side, then it is an oblique cylinder.
Surface Area of a Circular Cylinder Formula
A cylinder has a curved surface, and it has two types of surface areas: the curved surface area and the total surface area.
Look at the cylinder below to see its surface area, height (h), and radius (r).
A cylinder has two types of surface areas: Curved Surface Area of a Cylinder Total Surface Area of a Cylinder
Curved Surface Area of a Cylinder
The curved surface area of a cylinder is the area of the side that connects the two circular bases.
The formula for the CSA (Curved Surface Area) of the 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.
Total Surface Area of a Cylinder
The total area occupied by the cylinder, including the area of the curved surface and the area of the two circular bases, is known as the total surface area of the cylinder.
The total surface area of a cylinder is calculated by using the formula:
Total surface area = 2𝜋r(r + h) square units
Where r is the radius of the base of the cylinder. h is the height of the cylinder.
Derivation of the Total Surface Area of a Cylinder
To find the total surface area of a cylinder, imagine unfolding it.
The curved surface becomes a rectangle, and the bases are circles.
Let us take a cylinder with height (h) and radius of the base (r).
Total surface area of a cylinder = area of the curved surface + area of the two bases
Here, the base area of a cylinder = 𝜋r²
Curved surface area of a cylinder = 2𝜋rh
Substituting the formulas into the total surface area,
Total surface area of a cylinder, T = 2𝜋r² + 2𝜋rh
Take the common terms out: T = 2𝜋r(r + h)
Therefore, the total surface area of a cylinder T = 2𝜋r(r + h)
Volume of a Cylinder
The volume of a cylinder shows how much space is inside it. It tells us how much space is inside the cylinder or how much it can hold.
The volume of a cylinder can be found by using the formula: Volume = 𝜋r²h (cubic unit)
Confusion between CSA and TSA
Students assume that the curved surface area (CSA) and the total surface area (TSA) of a cylinder are the same.
This confusion arises because both involve the height and the radius.
Always remember that CSA is used on only the curved side of the cylinder, and TSA includes the curved surface and the bases.
Mistake 1
Forgetting to include both base areas in the total surface area
Students often calculate only the curved surface and forget to add the areas of both circular bases. Always include both parts when calculating the total surface area. Total surface area = curved surface area + area of two bases.
Mistake 2
Using the wrong value for 𝜋
A common mistake of students is using 22 as the value of 𝜋. Instead, use accurate values like 22/7 or 3.14. 𝜋 is a special number in math, and using the correct value is important for getting the right answer.
Mistake 3
Mixing up height and slant height
In cylinders, height refers to the perpendicular distance between the bases. There is no slant height in a cylinder, unlike a cone. Ensure the correct height is used in calculations.
Mistake 4
Assuming curved surface area and lateral surface area are different
Some students mistakenly believe that curved surface area and lateral surface area are different, but in a cylinder, they mean the same thing. So, use the same formula for both.
Mistake 5
Solved Examples of Surface Area of Circular Cylinder
Find the curved surface area of a cylinder with a radius of 5 cm and a height of 12 cm.
CSA = 377 cm²
Problem 1
Given r = 5 cm, h = 12 cm. Use the formula: CSA = 2𝜋rh = 2 × (22/7) × 5 × 12 = (44/7) × 60 = 377.14 cm² ≈ 377 cm²
Find the total surface area of a cylinder with a radius of 4 cm and a height of 10 cm.
Explanation
TSA = 352 cm²
Problem 2
Use the formula: TSA = 2𝜋r(r + h) = 2 × 3.14 × 4 × (4 + 10) = 2 × 3.14 × 4 × 14 = 2 × 3.14 × 56 = 351.68 cm² ≈ 352 cm²
A cylinder has a radius of 3 cm and a height of 8 cm. Find the total surface area.
Explanation
TSA = 207.36 cm²
Problem 3
Use the TSA formula: TSA = 2𝜋r(r + h) = 2 × 3.14 × 3 × (3 + 8) = 2 × 3.14 × 3 × 11 = 2 × 3.14 × 33 = 207.36 cm²
Find the curved surface area of a cylinder with a radius of 7 cm and a height of 15 cm.
Explanation
CSA = 660 cm²
Problem 4
CSA = 2𝜋rh = 2 × (22/7) × 7 × 15 = 2 × 22 × 15 = 660 cm²
The height of a cylinder is 20 cm, and its curved surface area is 440 cm². Find the radius.
Explanation
Radius = 3.5 cm
It is the total area that covers the outside of the cylinder, including its curved side and the two bases.
1.What are the two types of surface area in a cylinder?
2.What is the difference between height and slant height in a cylinder?
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 a Cylinder
Students often make mistakes while calculating the surface area of a cylinder, which leads to wrong 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
