105 LearnersLast updated on August 30, 2025
Surface Area of Closed Cylinder
A closed cylinder is a 3-dimensional shape with two parallel circular bases and a curved surface connecting them. The surface area of a closed cylinder is the total area covered by its outer surface, including both its curved surface and its two circular bases. In this article, we will learn about the surface area of a closed cylinder.
What is the Surface Area of a Closed Cylinder?
The surface area of a closed cylinder is the total area occupied by the boundary or surface of the cylinder. It is measured in square units.
A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.
The surface area of a closed cylinder includes the area of the curved surface and the areas of the two circular bases.
Cylinders are classified into right circular cylinders and oblique cylinders.
A right circular cylinder has its axis perpendicular to its bases, while an oblique cylinder has its axis tilted.
Surface Area of a Closed Cylinder Formula
A closed cylinder has both a curved surface area and two base areas.
Look at the cylinder below to see its surface area, height (h), and radius (r).
A closed cylinder has:
Curved Surface Area of a Cylinder
Total Surface Area of a Closed Cylinder
Curved Surface Area of a Cylinder
The area of the curved part of the cylinder, excluding its bases, is known as the curved surface area of a cylinder.
The curved surface area (CSA) of a cylinder is given by the formula:
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 Closed Cylinder
The total area occupied by the cylinder, including the area of the curved surface and the areas of the two circular bases, is known as the total surface area of a closed cylinder.
The total surface area (TSA) is calculated 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 Closed Cylinder To find the total surface area of a closed cylinder, consider the curved surface and the two circular bases.
Total surface area of a closed cylinder = base area + curved surface area + base area
Here, the base area of the cylinder = πr²
Curved surface area of the cylinder = 2πrh
Substituting the formulas into the total surface area,
Total surface area = 2πr² + 2πrh
Take the common terms out: TSA = 2πr(r + h)
Volume of a Cylinder
The volume of a cylinder shows how much space is inside it. It is the product of the area of the base and the height.
The volume of a cylinder can be found by using the formula: Volume = πr²h (cubic units)
Confusion between CSA and TSA
Students assume that the curved surface area (CSA) and the total surface area (TSA) of a closed cylinder are the same. This confusion arises because both involve the height and the radius. Always remember that CSA is only for the curved side, while TSA includes the curved surface and both bases.
Mistake 1
Using diameter instead of radius
Some students mistakenly use the diameter instead of the radius when calculating the surface area. Remember to use the radius in the formulas: CSA = 2πrh and TSA = 2πr(r + h).
Mistake 2
Using the wrong value for π
A common mistake 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
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 + 2 × base area.
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 Closed Cylinder
Find the curved surface area of a cylinder with a radius of 7 cm and a height of 10 cm.
CSA = 440 cm²
Problem 1
Given r = 7 cm, h = 10 cm. Use the formula: CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm²
Find the total surface area of a cylinder with a radius of 5 cm and a height of 13 cm.
Explanation
TSA = 565.2 cm²
Problem 2
Use the formula: TSA = 2πr(r + h) = 2 × 3.14 × 5 × (5 + 13) = 2 × 3.14 × 5 × 18 = 565.2 cm²
A cylinder has a radius of 6 cm and a height of 8 cm. Find the total surface area.
Explanation
TSA = 528 cm²
Problem 3
Use the TSA formula: TSA = 2πr(r + h) = 2 × 3.14 × 6 × (6 + 8) = 2 × 3.14 × 6 × 14 = 528 cm²
Find the curved surface area of a cylinder with a radius of 3.5 cm and a height of 5 cm.
Explanation
CSA = 110 cm²
Problem 4
CSA = 2πrh = 2 × (22/7) × 3.5 × 5 = 110 cm²
The height of a cylinder is 15 cm, and its curved surface area is 660 cm². Find the radius.
Explanation
Radius = 7 cm
It is the total area that covers the outside of the cylinder, including its curved surface and the two circular bases.
1.What are the two types of surface area in a cylinder?
2.What is the difference between diameter and radius?
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 Closed Cylinder
Students often make mistakes while calculating the surface area of a closed cylinder, which leads to incorrect answers. Below are some common mistakes and 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
