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124 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Hollow Cylinder
A hollow cylinder consists of two cylindrical surfaces, an inner and an outer surface, with both contributing to the lateral surface area. Imagine a drinking straw, where the material forms the lateral surface area, while the ends remain open and are not part of the lateral area calculation.
What is the Lateral Surface Area of a Hollow Cylinder?
The lateral surface area of a hollow cylinder is the area of the outer cylindrical surface minus the inner cylindrical surface, representing the area of the material that forms the cylinder.
Formula for Lateral Surface Area of a Hollow Cylinder
We can find the lateral surface area of a hollow cylinder using the inner radius “rโ,” the outer radius “rโ,” and the height “h” of the cylinder.
The lateral surface area is calculated using the formula: Area = 2๐ h(rโ - rโ).
How to Find Lateral Surface Area of a Hollow Cylinder
To find the lateral surface area of a hollow cylinder, follow these steps:
Step 1: Note the given parameters, including the inner and outer radii and the height.
Step 2: Ensure that all measurements are in the same unit before calculation.
Step 3: Use the equation, Area = 2๐ h(rโ - rโ), to find the lateral surface area of the hollow cylinder.
Step 4: Provide the calculated answer in square units.
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Common Mistakes and How to Avoid Them in the Lateral Surface Area of a Hollow Cylinder
There are a few common mistakes people make while calculating the lateral surface area of a hollow cylinder.
Some of them are listed below:
Mistake 1
Confusing the outer radius with the inner radius
Ensure you correctly identify which radius is the inner and which is the outer, as this affects the calculation of the material area.
Mistake 2
Incorrect subtraction of radii
Always subtract the inner radius from the outer radius to find the thickness of the material.
Mistake 3
Not mentioning the units with the numerical value
Always include the unit with your answer, even if the question doesn't specify it.
Use “square units” as a standard representation.
Mistake 4
Rounding in earlier steps
Avoid rounding intermediate values; round only the final answer to the required decimal places.
Mistake 5
Mistaking lateral surface area for total surface area
Remember, the lateral surface area is only the curved surface area excluding the top and bottom surfaces.
Solved Examples on Lateral Surface Area of a Hollow Cylinder
Problem 1
What is the lateral surface area of a hollow cylinder with an outer radius = 5 cm, inner radius = 3 cm, and height = 10 cm?
125.6 cm²
Explanation
Given: Outer radius rโ = 5 cm, Inner radius rโ = 3 cm, Height h = 10 cm
LSA = 2๐ h(rโ - rโ) = 2×3.14×10×(5-3) = 125.6 cm²
Problem 2
If the height of a hollow cylinder is 15 cm, the outer radius is 6 cm, and the lateral surface area is 188.4 cmยฒ. Find the inner radius.
4 cm
Explanation
Given: Outer radius rโ = 6 cm, Height h = 15 cm, LSA = 188.4 cm²
Using the formula: LSA = 2๐ h(rโ - rโ)
188.4 = 2×3.14×15×(6-rโ)
188.4 = 94.2(6-rโ)
6-rโ = 2
rโ = 6-2 = 4 cm
Problem 3
Calculate the lateral surface area of a hollow cylinder with an outer radius of 10 cm, an inner radius of 8 cm, and a height of 5 cm.
62.8 cm²
Explanation
Given: Outer radius rโ = 10 cm, Inner radius rโ = 8 cm, Height h = 5 cm
LSA = 2๐ h(rโ - rโ) = 2×3.14×5×(10-8) = 62.8 cm²
Problem 4
Determine the height of a hollow cylinder if its outer radius is 7 cm, its inner radius is 5 cm, and its lateral surface area is 150.72 square units.
4 units
Explanation
Given: Outer radius rโ = 7 units, Inner radius rโ = 5 units, LSA = 150.72 square units
Using the formula: LSA = 2๐ h(rโ - rโ)
150.72 = 2×3.14×h×(7-5)
150.72 = 12.56h
h = 150.72/12.56 = 12 units
Problem 5
The lateral surface area of a hollow cylinder is 314 cmยฒ. If its inner radius is 4 cm and height is 10 cm, find its outer radius.
6 cm
Explanation
Given: Inner radius rโ = 4 cm, Height h = 10 cm, LSA = 314 cm²
Using the formula: LSA = 2๐ h(rโ - rโ) 314 = 2×3.14×10×(rโ-4)
314 = 62.8(rโ-4)
rโ-4 = 5
rโ = 9 cm
FAQโs on Lateral Surface Area of a Hollow Cylinder
1.What is Lateral Surface Area?
2.How to calculate the lateral surface area?
3.Is lateral surface area and curved surface area the same?
4.What is the relation between the outer and inner radius?
5.How does the LSA change if the radius is doubled?
Important Glossary for Lateral Surface Area
- Outer radius: The distance from the center to the outer surface of the cylinder.
- Inner radius: The distance from the center to the inner surface of the cylinder.
- Height: The perpendicular distance between the bases of the cylinder.
- Pi (๐ ): A mathematical constant approximately equal to 3.14 used in calculations involving circles.
- Units: The standard measurement for expressing area, typically in square units.
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
