Surface Area of Closed Cylinder
2026-02-28 13:37 Diff
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Last updated on August 30, 2025

A closed cylinder is a 3-dimensional shape with two parallel circular bases and a curved surface connecting them. The surface area of a closed cylinder is the total area covered by its outer surface, including both its curved surface and its two circular bases. In this article, we will learn about the surface area of a closed cylinder.

What is the Surface Area of a Closed Cylinder?

The surface area of a closed 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 connected by a curved surface.

The surface area of a closed cylinder includes the area of the curved surface and the areas of the two circular bases.

Cylinders are classified into right circular cylinders and oblique cylinders.

A right circular cylinder has its axis perpendicular to its bases, while an oblique cylinder has its axis tilted.

Surface Area of a Closed Cylinder Formula

A closed cylinder has both a curved surface area and two base areas.

Look at the cylinder below to see its surface area, height (h), and radius (r).

A closed cylinder has:

Curved Surface Area of a Cylinder

Total Surface Area of a Closed Cylinder

Curved Surface Area of a Cylinder

The area of the curved part of the cylinder, excluding its bases, is known as the curved surface area of a cylinder.

The curved surface area (CSA) of a cylinder is given by the formula:

Curved Surface Area = 2πrh square units

Here, r is the radius of the base of the cylinder. h is the height of the cylinder.

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Total Surface Area of a Closed Cylinder

The total area occupied by the cylinder, including the area of the curved surface and the areas of the two circular bases, is known as the total surface area of a closed cylinder.

The total surface area (TSA) is calculated using the formula:

Total surface area = 2πr(r + h) 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 Closed Cylinder To find the total surface area of a closed cylinder, consider the curved surface and the two circular bases.

Total surface area of a closed cylinder = base area + curved surface area + base area

Here, the base area of the cylinder = πr²

Curved surface area of the cylinder = 2πrh

Substituting the formulas into the total surface area,

Total surface area = 2πr² + 2πrh

Take the common terms out: TSA = 2πr(r + h)

Volume of a Cylinder

The volume of a cylinder shows how much space is inside it. It is the product of the area of the base and the height.

The volume of a cylinder can be found by using the formula: Volume = πr²h (cubic units)

Confusion between CSA and TSA

Students assume that the curved surface area (CSA) and the total surface area (TSA) of a closed cylinder are the same. This confusion arises because both involve the height and the radius. Always remember that CSA is only for the curved side, while TSA includes the curved surface and both bases.

Problem 1

Given r = 7 cm, h = 10 cm. Use the formula: CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm²

Okay, lets begin

Find the total surface area of a cylinder with a radius of 5 cm and a height of 13 cm.

Explanation

TSA = 565.2 cm²

Well explained 👍

Problem 2

Use the formula: TSA = 2πr(r + h) = 2 × 3.14 × 5 × (5 + 13) = 2 × 3.14 × 5 × 18 = 565.2 cm²

Okay, lets begin

A cylinder has a radius of 6 cm and a height of 8 cm. Find the total surface area.

Explanation

TSA = 528 cm²

Well explained 👍

Problem 3

Use the TSA formula: TSA = 2πr(r + h) = 2 × 3.14 × 6 × (6 + 8) = 2 × 3.14 × 6 × 14 = 528 cm²

Okay, lets begin

Find the curved surface area of a cylinder with a radius of 3.5 cm and a height of 5 cm.

Explanation

CSA = 110 cm²

Well explained 👍

Problem 4

CSA = 2πrh = 2 × (22/7) × 3.5 × 5 = 110 cm²

Okay, lets begin

The height of a cylinder is 15 cm, and its curved surface area is 660 cm². Find the radius.

Explanation

Radius = 7 cm

Well explained 👍

It is the total area that covers the outside of the cylinder, including its curved surface and the two circular bases.

1.What are the two types of surface area in a cylinder?

Curved surface area and total surface area are the two types of surface area in a cylinder.

2.What is the difference between diameter and radius?

The radius is the distance from the center of the base to its edge, while the diameter is twice the radius.

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

Yes, in cylinders, both curved and lateral surface area mean the same.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

Common Mistakes and How to Avoid Them in the Surface Area of a Closed Cylinder

Students often make mistakes while calculating the surface area of a closed cylinder, which leads to incorrect answers. Below are some common mistakes and 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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