Surface Area of Cylinder: Formulas, Key Differences on TSA & CSA

Surface Area of Cylinder:  A cylinder is a three-dimensional shape with two flat circular ends and a curved side that connects them. The surface area of a cylinder is the total space covered by its outer surface.

Learning about the surface area of a cylinder is important for kids because it helps them understand basic math ideas about shapes and measurements. It also teaches them how to solve real-world problems, like figuring out how much material is needed to make objects like cans, pipes, or tanks.

This topic improves their math skills and helps them think logically and solve problems step by step. To make it easy for students, we have explained the surface area of a cylinder, its formula, types, and how to calculate it below.

Check Out - Area of Rectangle

What is Surface Area of Cylinder?

A cylinder is a 3D shape with two flat circular bases connected by a curved surface. The distance between the two bases is the cylinder's height, while the radius is the distance from the center to the edge of each circular base. It is a common shape in everyday objects like cans and pipes.

The surface area of a 3D object is the total space covered by its outer surface and is measured in square units such as square centimeters or square inches.

The surface area of a cylinder includes the area of its two circular bases and the curved surface connecting them. In simple terms, it is the total area you would cover if you were to wrap or paint the entire cylinder. Understanding the surface area helps in practical tasks, such as calculating material requirements for cylindrical objects or solving math problems.

Surface Area of Cylinder Formula

The surface area of a cylinder is calculated using formulas that measure the space covered by its curved side and its circular bases. A cylinder has two main types of surface areas:

CSA = 2πrh

• r = radius of the circular base
• h = height of the cylinder
• π (Pi) = 3.14159 (approximately)

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TSA = 2πr(r + h)

• r = radius of the circular bases
• h = height of the cylinder
• π (Pi) = 3.14159 (approximately)

Total Surface Area of Cylinder

The total surface area TSA of cylinder includes the area of its curved surface and the areas of its two circular bases. Knowing the TSA is important for practical purposes, like determining the material needed to make objects such as cans, pipes, or tanks.

Formula:

• r = radius of the circular bases
• h = height of the cylinder
• π = Pi, a constant approximately equal to 3.14159

Check Out - Area of a Circle

Parts of the Total Surface Area (TSA):

• Area of one base = πr²
• Combined area of both bases = 2πr²

• Height = h (height of the cylinder)
• Width = 2πr (circumference of the base)

Calculation of Total Surface Area:

TSA of Cylinder = Area of bases + Curved surface area TSA = 2πr² + 2πrh TSA = 2πr(r + h)

For example, if a cylinder has a radius of 5 cm and a height of 10 cm, the total surface area can be calculated as: TSA = 2 × 3.14159 × 5 × (10 + 5) = 31.4159 × 15 ≈ 471.24 square cm.

Check Out -  Area of a Sector

Curved Surface Area of Cylinder

The curved surface area (CSA) of a cylinder, also called the lateral surface area , is the area of the cylindrical sides that wrap around the cylinder. It does not include the areas of the top and bottom circular bases. Knowing the curved surface area is useful for tasks like determining how much material is needed to wrap around a cylinder without covering its bases.

CSA = 2πrh

• r is the radius of the circular base
• h is the height of the cylinder
• π (Pi) is approximately 3.14159

• The height of the rectangle is the same as the cylinder’s height (h).
• The width of the rectangle is the circumference of the circular base , calculated as 2πr.

The area of this rectangle (representing the curved surface area) is: Area = height × circumference = h × 2πr = 2πrh

How to Calculate the Surface Area of Cylinder?

The surface area of a cylinder is determined by summing the areas of its two circular bases and the area of its curved surface. The following is a step-by-step guide on how to calculate it:

Area (bases) = π × radius × radius (or πr²)

Area (bases) = 2  × πr²

2. Find the area of the curved surface (lateral surface): The curved surface can be "unfolded" into a rectangle. The height of the rectangle is the height h of the cylinder, and the width is the circumference of the base, which is 2πr. So, the lateral area is:

Area (lateral) = 2πr × h or 2πrh

Total Surface Area = 2πr² + 2πrh

Total Surface Area = 2πr(r + h)

Differences Between TSA and CSA of Cylinder

Key Differences:

• TSA of cylinder includes both the lateral surface and the areas of the circular bases, while CSA of cylinder includes only the lateral (curved) surface.
• TSA is greater than CSA because it accounts for more surface area (the two bases are included in TSA but not in CSA). Join Online Tuition Classes for Kids Now