Surface Area of a Cylinder: An In-depth Explanation

If you had to rank the most ubiquitous shapes in existence, the cylinder would be among the top tiers. From soda cans and water bottles to fire extinguishers, this shape not only plays an integral role in our daily lives but is also a fundamental shape in many fields, including engineering. This blog dissects one key aspect—the Surface Area of a Cylinder, which measures the total area that the surface of a cylindrical object occupies. So read on, master the mathematics behind Cylinders and deepen your appreciation for this important shape!

Table of Contents 

1) What is the Surface Area of a Cylinder? 

2) Formula for Surface Area of a Cylinder 

3) Steps to Calculate the Surface Area of a Cylinder 

4) Total Surface Area of Cylinder (TSA)

5) Conclusion 

What is the Surface Area of a Cylinder? 

A Cylinder is a 3D figure with two circular bases that are parallel and connected by a curved surface. It can be visualised as a series of stacked circles, all identical in size, arranged in a straight line. The Surface Area of a Cylinder is the area covering the outer surface of a Cylinder. To calculate a Cylinder's total surface area, you must find the area of the three parts of its surface and add them.  
 

Formula for Surface Area of a Cylinder 

The Surface Area of a Cylinder is the total area covered by its two circular bases and the curved surface that wraps around them. The formula for calculating the Surface Area of a Cylinder is given by: 

Where: 

r = radius of the circular base. 

h = the height of the Cylinder. 

π is a constant approximately equal to 3.14159. 

This formula combines the areas of the two circular bases  

and the curved surface area 2πrh 
 

Steps to Calculate the Surface Area of a Cylinder 

Calculating the Surface Area of a Cylinder involves a few straightforward steps: 

1) Measure the Radius and Height: Start by measuring the radius of the base (r) and the height (h) of the Cylinder. 

2) Apply the Formula: Plug the values of r and h into the surface area formula: 2πr (h + r). 

3) Calculate: Perform the calculations by multiplying and adding as per the formula. Don't forget to square the radius where necessary and multiply by π. 

4) Interpret the Results: The result will give you the surface area in square units (e.g., square centimetres, square metres). 

Take the leap! Equip yourself with the latest engineering skills and stand out in the job market. Register for our Engineering Skills Training today!

Total Surface Area of Cylinder (TSA)

Before we dive into the total Surface Area of a Cylinder, it’s important to consider the following points:

1) The curved Surface Area of a Cylinder is a rectangle

2) The circumference of the circle is the rectangle's length 

3) The height of the Cylinder is the rectangle's height

So, the total surface area will be the sum of the area of the two circles and the curved surface area.

Where

r = Radius of the circle

h = Height of the Cylinder

2πrh = Curved surface area

πr2 = Area of the circle

Practical Examples of Cylinder Surface Area Calculation 

Let’s explore some practical examples to solidify our understanding of how to calculate the Surface Area of a Cylinder. 

Example 1: Calculating the Curved Surface Area 

Suppose you have a Cylinder whose radius is 3 cm and height is 7 cm. The first step is to calculate the curved surface area, which is given by the formula: 

Substitute the given values: 

So, the curved surface area is 131.95 square centimetres 

Example 2: Curved Surface Area Expressed in Terms of π 

For a more general form, suppose the Cylinder's radius is 5 units, and the height is 10 units. The curved surface area can be expressed in terms of π: 

Here, the surface area is left in terms of π, making it more convenient for further mathematical operations. 

Example 3: Finding the Total Surface Area 

Now, let’s find the total surface area of a Cylinder where the radius is 4 cm, and the height is 9 cm. Using the surface area formula: 

Substitute the values: 

Thus, the total surface area is 326.73 square centimetres. 

Become the best version of you! Unlock your potential with our Personal Development Training and start your transformation today!

What is the Cross-sectional Area of a Cylinder?

The cross-sectional area of a Cylinder generally refers to the circular shape as seen from top.

What is the Difference Between Surface Area and Cross-sectional Area?

Area is the space used by an object when it is resting on a surface. Meanwhile, a cross-section is obtained when the same object is cut into two pieces. The area of that cross-section is known as the cross-sectional area.

Conclusion 

Understanding how to calculate the Surface Area of a Cylinder is an essential skill in geometry. Whether you're working with physical objects or solving theoretical problems, the ability to determine the surface area can be highly beneficial. The formulas and calculations outlined in this blog will help you tackle any technical challenges related to Cylinders. 

Shape your future today. Our Career Development Course is the boost you need; register now and take charge of your career path!