106 LearnersLast updated on August 5th, 2025
Surface Area of Right Circular Cylinder
A right circular cylinder is a 3-dimensional shape with two parallel circular bases connected by a curved surface. The surface area of the cylinder is the total area covered by its outer surface. The surface area of the cylinder includes both its curved surface and its circular bases. In this article, we will learn about the surface area of a right circular cylinder.
What is the Surface Area of a Right Circular Cylinder?
The surface area of a right circular 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 identical flat ends that are circular and a curved surface connecting them. The axis of the cylinder is the line joining the centers of the two bases.
The surface area of a cylinder can be divided into two parts: the curved surface area and the total surface area.
Surface Area of a Right 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 area of the curved part of the cylinder, excluding its bases, is known as the curved surface area of a cylinder.
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 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 unit 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 unrolling the curved surface into a rectangle. The width of the rectangle is equal to the circumference of the base, and the height of the rectangle is the height of the cylinder.
The total surface area of a cylinder = base area of the cylinder + curved surface area of the cylinder.
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 the 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
Using diameter instead of radius
Some students mistakenly use the diameter instead of the radius when finding the surface area. Remember to use the radius, which is half of the diameter.
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
Forgetting to include the base areas in the total surface area
Students often calculate only the curved surface and forget to add the 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 a Right Circular Cylinder
Find the curved surface area of a cylinder with a radius of 6 cm and a height of 12 cm.
CSA = 452.16 cm²
Problem 1
Given r = 6 cm, h = 12 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 6 × 12 = 452.16 cm²
Find the total surface area of a cylinder with a radius of 4 cm and a height of 10 cm.
Explanation
TSA = 351.68 cm²
Problem 2
Use the formula: TSA = 2πr(r + h) = 2 × 3.14 × 4 × (4 + 10) = 2 × 3.14 × 4 × 14 = 351.68 cm²
A cylinder has a radius of 5 cm and a height of 15 cm. Find the total surface area.
Explanation
TSA = 628 cm²
Problem 3
Use the TSA formula: TSA = 2πr(r + h) = 2 × 3.14 × 5 × (5 + 15) = 2 × 3.14 × 5 × 20 = 628 cm²
Find the curved surface area of a cylinder with a radius of 3 cm and a height of 8 cm.
Explanation
CSA = 150.72 cm²
Problem 4
CSA = 2πrh = 2 × 3.14 × 3 × 8 = 150.72 cm²
The height of a cylinder is 10 cm, and its curved surface area is 314 cm². Find the radius.
Explanation
Radius = 5 cm
It is the total area that covers the outside of the cylinder, including its curved side and the bases.
1.What are the two types of surface area in a cylinder?
2.What is the difference between radius and diameter?
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.
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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.
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: She has songs for each table which helps her to remember the tables
