111 LearnersLast updated on August 5th, 2025
Surface Area of Solid Cylinder
A cylinder is a 3-dimensional shape with two parallel circular bases and a curved surface connecting them. 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 its two bases. In this article, we will learn about the surface area of a solid cylinder.
What is the Surface Area of a Solid Cylinder?
The surface area of a solid 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 and a curved surface.
It has three surface areas: the area of the curved surface and the areas of the two bases. Cylinders are commonly seen in everyday objects like cans and tubes.
Surface Area of a Cylinder Formula
A cylinder has a curved surface and two circular bases. Therefore, it has three components to its surface area: the curved surface area and the areas of the two circular bases.
Look at the cylinder below to understand its surface area, height (h), and radius (r).
Curved Surface Area of a Cylinder
The curved surface area of a cylinder refers to the area of the outer surface that wraps around the sides of the cylinder, excluding the bases.
The formula for the curved surface area (CSA) of a cylinder is given as: Curved Surface Area = 2πrh square units Here, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Total Surface Area of a Cylinder
The total surface area of a cylinder includes the curved surface area and the area of the two circular bases.
The total surface area of a cylinder is calculated using the formula: Total surface area = 2πr(r + h) square units Where r is the radius of the base of the cylinder, and 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, consider the curved surface and the two bases. The curved surface, when unrolled, forms a rectangle with a width equal to the height of the cylinder and a length equal to the circumference of the base.
The area of the rectangle (curved surface) is 2πrh, and the area of each base is πr².
Total surface area of a cylinder = 2 × base area + curved surface area
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 indicates how much space is inside it. It tells us how much a cylinder can hold. The volume of a cylinder can be found 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 only for the curved side of the cylinder, and 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 that the formulas use the radius, which is half of the diameter.
Mistake 2
Using the wrong value for π
A common mistake students make 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 area of the two circular bases. Always include both parts when calculating the total surface area. Total surface area = curved surface area + 2 × base area.
Mistake 4
Assuming the curved surface area includes the bases
Some students mistakenly believe that the curved surface area includes the bases, but in a cylinder, it only refers to the side that wraps around. Use the appropriate formula for each part.
Mistake 5
Solved Examples of Surface Area of Solid 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 × 3.14 × 5 × 12 = 377 cm²
Find the total surface area of a cylinder with a radius of 4 cm and height 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 = 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 = 207.36 cm²
Find the curved surface area of a cylinder with a radius of 2.5 cm and a height of 6 cm.
Explanation
CSA = 94.2 cm²
Problem 4
CSA = 2πrh = 2 × 3.14 × 2.5 × 6 = 94.2 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 two bases.
1.What are the components of the surface area in a cylinder?
2.What is the difference between diameter and radius?
3.Is the curved surface area the same as the 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 incorrect 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
