Surface Area of a Cylinder: Formula & Examples

Let’s learn how to determine the surface area of a cylinder.

What is a Cylinder?

A cylinder is a tube-shaped object with two same-sized circular bases, parallel straight sides, and a circular or oval cross-section. Its height is the distance between the two bases, while the radius is the distance from the center of a base to any point on the same base. Examples of cylinder-shaped objects are soda cans and pipes. 

Related Reading: Volume of a Cylinder – Formula & Examples

How to Find the Surface Area of a Cylinder:

To find the surface area of a cylinder, add up the areas of the bases and the area of the rectangular surface, as expressed in this formula.

SA=2πr²+2πrh where h=height and π = 3.14

Surface area (SA or S) is measured in square units, such as square meters (m²), square centimeters (cm²), and square inches (in²).

To better understand a cylinder’s surface area, imagine a soda can with its label or wrapper unrolled. Spreading the label gives us a rectangle (See illustration below). As you may recall, circumference
(C = 2πr) refers to the curved length around the circle, so “uncurving” the bases (label) would give you the length of the rectangle. The rectangle’s width is the same as the height of the cylinder.

Now that you have the rectangle’s length (2πr) and width (h), you can compute its area by multiplying them (2πr x h) but that will not give you the total surface area of the cylinder.

To find the total surface area of the cylinder, add the areas of the two circles and the area of the rectangle, as seen in the illustration above. This is how the formula was derived:

S=Area of base 1+Area of base 2+Area of rectangle

S=r²+πr²+L (W)

S=r²+πr²+(2πr) (h)

S=2r²+2πrh where: r2=area of the circle or base; 2πr=length of the surface obtained from the circle’s circumference; h=height of the cylinder or width of the surface 

Here’s a quick guide to finding the surface area of a cylinder:

Step 1. Write down the given figures. You’ll need the cylinder’s radius and height. Make sure all measurement units are the same. If not, convert either of them to match the other. 

Step 2. Plug the figures into the formula.

Step 3. Perform the operations. Don’t forget to write the cubit unit together with the answer.

Example 1: Find the Surface Area of a Cylinder when given Height and Radius

Find the surface area of the cylinder below.

Solution for Example 1:

Firstly, write down the given figures: radius (r = 2m) and height (h = 3m).

Next, substitute 2m for r and 3m for h into the equation.

S = 2πr² + 2πrh

S = 2π(2m)²+2π(2m)(3m)

Lastly, simplify.

S = 2π(4m²) + 2π(6m²)

S = 62.83…m²

Therefore, the surface area is about 62.83m².

Example 2: Find the Surface Area of a Cylinder when given Height and Radius

Find the surface area of the cylinder below.

Solution for Example 2:

Firstly, write down the given figures: the diameter (d = 3m) and height (h = 125cm). Recall that the formula requires the radius and not the diameter. So, divide the diameter (3m) by 2 to find the radius.

r = d/2 = 3m/2 = 1.5m

Next, let’s convert the height (125cm) to match the radius’ unit (m). Remember that 100cm = 1m.

h = 125cm/100cm = 1.25m

Finally, substitute 1.5m for r and 1.25m for h in the formula.

S = 2πr² + 2πrh

S = 2π(1.5m)²+2π(1.5m)(1.25m)

Simplify.

S = 2π(2.25m²) + 2π(1.875m²)

S = 25.91814…m²

Therefore, the surface area is about 25.92m².

Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the surface area of a cylinder.

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