Lateral Surface Area of a Hollow Cylinder
2026-02-28 19:05 Diff
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Last updated on December 11, 2025

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 “r₁,” the outer radius “r₂,” and the height “h” of the cylinder.

The lateral surface area is calculated using the formula: Area = 2𝝅h(r₂ - r₁).

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 = 2𝝅h(r₂ - r₁), 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:

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?

Okay, lets begin

125.6 cm²

Explanation

Given: Outer radius r₂ = 5 cm, Inner radius r₁ = 3 cm, Height h = 10 cm

LSA = 2𝝅h(r₂ - r₁) = 2×3.14×10×(5-3) = 125.6 cm²

Well explained 👍

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 cm². Find the inner radius.

Okay, lets begin

4 cm

Explanation

Given: Outer radius r₂ = 6 cm, Height h = 15 cm, LSA = 188.4 cm²

Using the formula: LSA = 2𝝅h(r₂ - r₁)

188.4 = 2×3.14×15×(6-r₁)

188.4 = 94.2(6-r₁)

6-r₁ = 2

r₁ = 6-2 = 4 cm

Well explained 👍

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.

Okay, lets begin

62.8 cm²

Explanation

Given: Outer radius r₂ = 10 cm, Inner radius r₁ = 8 cm, Height h = 5 cm

LSA = 2𝝅h(r₂ - r₁) = 2×3.14×5×(10-8) = 62.8 cm²

Well explained 👍

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.

Okay, lets begin

4 units

Explanation

Given: Outer radius r₂ = 7 units, Inner radius r₁ = 5 units, LSA = 150.72 square units

Using the formula: LSA = 2𝝅h(r₂ - r₁)

150.72 = 2×3.14×h×(7-5)

150.72 = 12.56h

h = 150.72/12.56 = 12 units

Well explained 👍

Problem 5

The lateral surface area of a hollow cylinder is 314 cm². If its inner radius is 4 cm and height is 10 cm, find its outer radius.

Okay, lets begin

6 cm

Explanation

Given: Inner radius r₁ = 4 cm, Height h = 10 cm, LSA = 314 cm²

Using the formula: LSA = 2𝝅h(r₂ - r₁) 314 = 2×3.14×10×(r₂-4)

314 = 62.8(r₂-4)

r₂-4 = 5

r₂ = 9 cm

Well explained 👍

FAQ’s on Lateral Surface Area of a Hollow Cylinder

1.What is Lateral Surface Area?

The lateral surface area of a hollow cylinder is the area of the material forming the curved part of the cylinder, excluding the top and bottom surfaces.

2.How to calculate the lateral surface area?

The lateral surface area of a hollow cylinder can be calculated using the formula: Area = 2𝝅h(r₂ - r₁).

3.Is lateral surface area and curved surface area the same?

Yes, for a hollow cylinder, they both refer to the curved material area excluding the top and bottom surfaces.

4.What is the relation between the outer and inner radius?

The outer radius is the distance from the center to the outer surface, while the inner radius is the distance from the center to the inner surface.

5.How does the LSA change if the radius is doubled?

If both inner and outer radii are doubled, the difference remains the same, so the LSA depends on the height and the difference between the radii.

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 (𝝅): A mathematical constant approximately equal to 3.14 used in calculations involving circles.
  • Units: The standard measurement for expressing area, typically in square units.

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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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