102 LearnersLast updated on August 5th, 2025
Surface Area of Hollow Cylinder
A hollow cylinder is a 3-dimensional shape with two circular bases and a cylindrical surface, but it has an empty space inside. The surface area of a hollow cylinder includes the inner and outer curved surfaces and the areas of the two circular bases. In this article, we will learn about the surface area of a hollow cylinder.
What is the Surface Area of a Hollow Cylinder?
The surface area of a hollow cylinder is the total area occupied by the outer and inner surfaces of the cylinder, along with the areas of the two circular bases. It is measured in square units.
A hollow cylinder is a 3D shape formed by two coaxial cylinders. It has a curved outer surface, a curved inner surface, and two circular bases, making up three distinct surface areas: the outer curved surface area, the inner curved surface area, and the total surface area including the bases.
Surface Area of a Hollow Cylinder Formula
A hollow cylinder has three types of surface areas: the outer curved surface area, the inner curved surface area, and the total surface area.
Look at the hollow cylinder below to see its surface area, height(h), outer radius(R), and inner radius(r).
A hollow cylinder has three types of surface areas:
Outer Curved Surface Area of a Hollow Cylinder
Inner Curved Surface Area of a Hollow Cylinder
Total Surface Area of a Hollow Cylinder
Outer Curved Surface Area of a Hollow Cylinder
The outer curved surface area of a hollow cylinder is the area of the cylindrical surface on the outside.
The formula for the outer curved surface area (OCSA) is given as: Outer Curved Surface Area = 2πRh square units
Here, R is the outer radius of the hollow cylinder. h is the height of the hollow cylinder.
Inner Curved Surface Area of a Hollow Cylinder
The inner curved surface area of a hollow cylinder is the area of the cylindrical surface on the inside.
The formula for the inner curved surface area (ICSA) is given as: Inner Curved Surface Area = 2πrh square units
Where r is the inner radius of the hollow cylinder. h is the height of the hollow cylinder.
Total Surface Area of a Hollow Cylinder
The total surface area of a hollow cylinder includes the inner and outer curved surfaces, as well as the areas of the two circular bases.
The total surface area is calculated by using the formula: Total Surface Area = 2πRh + 2πrh + 2π(R^2 - r^2) square units
This includes the outer curved surface area, the inner curved surface area, and the areas of the two circular annuli (the difference between the areas of the large and small circles).
Confusion between OCSA and ICSA
Students assume that the outer curved surface area (OCSA) and the inner curved surface area (ICSA) of a hollow cylinder are the same. This confusion arises because both involve the height and the radii. Always remember that OCSA uses the outer radius, while ICSA uses the inner radius.
Mistake 1
Using wrong radii for the bases
Sometimes students mistakenly use only one radius for calculating the base areas, forgetting that there are two different radii for the inner and outer bases. Always use R for the outer base and r for the inner base.
Mistake 2
Incorrectly calculating the base area difference
A common mistake is not subtracting the area of the inner base from the outer base when calculating the base areas. Always calculate the annular area as π(R^2 - r^2).
Mistake 3
Forgetting to sum all components for total surface area
Students often calculate only the curved surfaces and forget to add the areas of the bases. Always include the outer and inner curved surfaces and the annular bases when calculating the total surface area.
Mistake 4
Assuming the hollow cylinder reduces to a solid one
Some students mistakenly treat the hollow cylinder as a solid cylinder, ignoring the inner hollow part. Be sure to consider both the inner and outer surfaces in calculations.
Mistake 5
Solved Examples of Surface Area of Hollow Cylinder
Find the outer curved surface area of a hollow cylinder with an outer radius of 8 cm and a height of 12 cm.
OCSA = 603.2 cm²
Problem 1
Given R = 8 cm, h = 12 cm. Use the formula: OCSA = 2πRh = 2 × 3.14 × 8 × 12 = 603.2 cm²
Find the total surface area of a hollow cylinder with an outer radius of 10 cm, an inner radius of 7 cm, and a height of 15 cm.
Explanation
TSA = 1615.4 cm²
Problem 2
Use the formula: TSA = 2πRh + 2πrh + 2π(R² - r²) = 2 × 3.14 × 10 × 15 + 2 × 3.14 × 7 × 15 + 2 × 3.14 × (10² - 7²) = 942 + 658.8 + 395.6 = 1996.4 cm²
A hollow cylinder has an outer radius of 6 cm, an inner radius of 4 cm, and a height of 10 cm. Find the inner curved surface area.
Explanation
ICSA = 251.2 cm²
Problem 3
Use the formula: ICSA = 2πrh = 2 × 3.14 × 4 × 10 = 251.2 cm²
Find the total surface area of a hollow cylinder with an outer radius of 9 cm, an inner radius of 5 cm, and a height of 20 cm.
Explanation
TSA = 2970.4 cm²
Problem 4
Use the formula: TSA = 2πRh + 2πrh + 2π(R² - r²) = 2 × 3.14 × 9 × 20 + 2 × 3.14 × 5 × 20 + 2 × 3.14 × (9² - 5²) = 1130.4 + 628 + 251.2 = 2009.6 cm²
The inner curved surface area of a hollow cylinder is 440 cm², with an inner radius of 7 cm. Find the height.
Explanation
Height = 10 cm
It is the total area that covers the outside and inside of the hollow cylinder, including the curved surfaces and the annular bases.
1.What are the different surface areas in a hollow cylinder?
2.How do you find the total surface area of a hollow cylinder?
3.What is the formula for the annular base area of a hollow cylinder?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Hollow Cylinder
Students often make mistakes while calculating the surface area of a hollow 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
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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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