105 LearnersLast updated on August 5th, 2025
Surface Area of Right Cylinder
A right cylinder is a 3-dimensional shape with two parallel circular bases connected by a curved surface. The surface area of the right cylinder is the total area covered by its outer surface. This includes both the curved surface and the two circular bases. In this article, we will learn about the surface area of a right cylinder.
What is the Surface Area of a Right Cylinder?
The surface area of a right cylinder is the total area occupied by its outer surface, measured in square units.
A cylinder is a 3D shape with two parallel, congruent circular bases connected by a curved surface. The axis of a right cylinder is perpendicular to the bases.
The surface area of a right cylinder includes the area of the curved surface and the area of the two bases.
Surface Area of a Right Cylinder Formula
A right cylinder has a curved surface and two circular bases, resulting in two types of surface areas: the lateral surface area and the total surface area.
Look at the cylinder below to see its surface area, height (h), and radius (r).
A right cylinder has two types of surface areas:
- Lateral Surface Area of a Right Cylinder
- Total Surface Area of a Right Cylinder
Lateral Surface Area of a Right Cylinder
The area of the curved part of the cylinder, excluding its bases, is known as the lateral surface area of a cylinder. The formula for the LSA (Lateral Surface Area) of a right cylinder is given as:
Lateral 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 Right Cylinder
The total area occupied by the right 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 right cylinder is calculated using the formula: Total surface area = 2πr(h + r) 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 Right Cylinder
To find the total surface area of a right cylinder, imagine cutting it vertically and unfolding it. The curved surface becomes a rectangle, and the bases remain circles.
Let us take a right cylinder with height (h) and radius of the base (r). Total surface area of a right cylinder = base area of two circles + lateral surface area of a cylinder
Here, the base area of a cylinder = 2πr²
Lateral 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(h + r)
Therefore, the total surface area of a right cylinder T = 2πr(h + r)
Volume of a Right Cylinder
The volume of a right cylinder shows how much space is inside it. It can be calculated by using the formula: Volume = πr²h (cubic units)
Confusion between LSA and TSA
Students assume that the lateral surface area (LSA) 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 LSA is used on only the curved side of the cylinder, and TSA includes the curved surface and the bases.
Mistake 1
Using radius instead of diameter
Some students mistakenly use the diameter instead of the radius when finding the surface area. Remember that the formulas use the radius (half of the diameter), so ensure you use the correct measurement.
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 both base areas in the total surface area
Students often calculate only the lateral surface and forget to add the areas of both circular bases. Always include both parts when calculating the total surface area. Total surface area = lateral surface area + 2 × base area.
Mistake 4
Assuming lateral surface area and curved surface area are different
Some students mistakenly believe that lateral surface area and curved 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 Right Cylinder
Find the lateral surface area of a right cylinder with a radius of 4 cm and a height of 9 cm.
LSA = 226.08 cm²
Problem 1
Given r = 4 cm, h = 9 cm. Use the formula: LSA = 2πrh = 2 × 3.14 × 4 × 9 = 2 × 3.14 × 36 = 226.08 cm²
Find the total surface area of a right cylinder with a radius of 5 cm and a height of 12 cm.
Explanation
TSA = 534.6 cm²
Problem 2
Use the formula: TSA = 2πr(h + r) = 2 × 3.14 × 5 × (12 + 5) = 2 × 3.14 × 5 × 17 = 2 × 3.14 × 85 = 534.6 cm²
A right cylinder has a radius of 6 cm and a height of 10 cm. Find the total surface area.
Explanation
TSA = 603.84 cm²
Problem 3
Use the TSA formula: TSA = 2πr(h + r) = 2 × 3.14 × 6 × (10 + 6) = 2 × 3.14 × 6 × 16 = 2 × 3.14 × 96 = 603.84 cm²
Find the lateral surface area of a right cylinder with a radius of 3.5 cm and a height of 8 cm.
Explanation
LSA = 175.84 cm²
Problem 4
LSA = 2πrh = 2 × (22/7) × 3.5 × 8 = 2 × 22 × 0.5 × 8 = 22 × 8 = 175.84 cm²
The height of a right cylinder is 15 cm, and its lateral surface area is 660 cm². Find the radius.
Explanation
Radius = 7 cm
It is the total area that covers the outside of the right cylinder, including its curved side and the two bases.
1.What are the two types of surface area in a right cylinder?
2.What is the difference between lateral surface area and total surface area?
3.Is lateral surface area the same as curved surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Right Cylinder
Students often make mistakes while calculating the surface area of a right 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
