Surface Area of Solid Cylinder
2026-02-28 23:53 Diff
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Last updated on August 5, 2025

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.

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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.

Problem 1

Given r = 5 cm, h = 12 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 5 × 12 = 377 cm²

Okay, lets begin

Find the total surface area of a cylinder with a radius of 4 cm and height 10 cm.

Explanation

TSA = 352 cm²

Well explained 👍

Problem 2

Use the formula: TSA = 2πr(r + h) = 2 × 3.14 × 4 × (4 + 10) = 2 × 3.14 × 4 × 14 = 352 cm²

Okay, lets begin

A cylinder has a radius of 3 cm and a height of 8 cm. Find the total surface area.

Explanation

TSA = 207.36 cm²

Well explained 👍

Problem 3

Use the TSA formula: TSA = 2πr(r + h) = 2 × 3.14 × 3 × (3 + 8) = 2 × 3.14 × 3 × 11 = 207.36 cm²

Okay, lets begin

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

Well explained 👍

Problem 4

CSA = 2πrh = 2 × 3.14 × 2.5 × 6 = 94.2 cm²

Okay, lets begin

The height of a cylinder is 10 cm, and its curved surface area is 314 cm². Find the radius.

Explanation

Radius = 5 cm

Well explained 👍

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?

Curved surface area and the areas of the two circular bases are the components of the surface area in a cylinder.

2.What is the difference between diameter and radius?

The diameter is the distance across the circle through the center, while the radius is half of the diameter.

3.Is the curved surface area the same as the 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 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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