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Introduction

QUICK LINKS


Introduction

Surface Area of Cylinders

INTRO
The surface area of a 3D shape is equal to the sum of the areas of all the faces (sides) of that shape. A helpful way to think about it is:
surface area = sum of face areas
We can also think about surface area in terms of gifts! The surface area is like the minimum amount of wrapping paper we need to prep a gift for its surprise reveal. 🤩If we were to unwrap a gift, the amount of wrapping would be equal to the surface area of the object it was covering.
When we “unwrap” a 3D shape, we get what we call a net. A surface area net shows us the different 2D shapes that make up the faces of the 3D shape.
We can then find the area of each face and then add them all together to find the total surface area.

What is lateral surface area?

When working with pyramids, cylinders, and cones, you may also be asked to find the lateral surface area.
Lateral surface area is simply the total surface area of an object minus the area of its base(s).
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to find the surface area of cylinders and test your understanding.

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CALCULATOR

Surface Area of Cylinders Calculator

What is your shape?

Step 1. Unwrap the cylinder.

This gives us our net:

Step 2. Calculate the area of each part of the net that makes up the cylinder.

Sides that the are the same color are the same size 🎉.
ShapeArea
1
(Rectangle)
2
(Circle)
3
(Circle)

Step 3. Add up the areas of the shapes that make up the cylinder.

The surface area of this cylinder is .
KEY STEPS

How to Find Surface Area of Cylinders

Step 1. Unwrap the cylinder.

Step 2. Calculate the area of each part of the net that makes up the cylinder.

Rectangle
Circles

Step 3. Add up the areas of the shapes that make up the cylinder.

LESSON
Surface Area of Cylinders

Surface Area of Cylinders

The surface area of a cylinder is equal to the sum of the area of the top and bottom plus the area of the wall of the cylinder.
If we unwrap a cylinder, we can see that the net is made up of rectangle and identical circles.
So, we need to find the area of one of the circles and double it. Then we add it to the area of the rectangle to get the total surface area!This formula can be a little tricky to understand though 🤯.
The trick is to remember where the length and the width of the rectangle come from.
If we watch the cylinder unwrap, we can see that the length of the rectangle is equal to the circumference of the circle.
We can also see that the width of the rectangle is equal to the height of the cylinder:
When we multiply these two together, we get the area of the rectangle around a cylinder:
Then, we can add in the areas of the two circles to get the total surface area:

What about the lateral surface area?

If we wanted to find the lateral surface area of the cylinder, we would exclude the areas of the circular bases:
Let's unwrap some cylinders to practice finding their surface area!

EXAMPLE 1

Let's start here - find the surface area of this cylinder:
What is your shape?

Step 1. Unwrap the cylinder.

This gives us our net:

Step 2. Calculate the area of each part of the net that makes up the cylinder.

Now, we'll find the area of each shape in the net. Notice that some shapes have the same area:
Sides that the are the same color are the same size 🎉.
ShapeArea
1
(Rectangle)
2
(Circle)
3
(Circle)

Step 3. Add up the areas of the shapes that make up the cylinder.

The surface area of this cylinder is .

EXAMPLE 2

Nice work! Try another one:
What is your shape?

Step 1. Unwrap the cylinder.

This gives us our net:

Step 2. Calculate the area of each part of the net that makes up the cylinder.

Now, we'll find the area of each shape in the net. Notice that some shapes have the same area:
Sides that the are the same color are the same size 🎉.
ShapeArea
1
(Rectangle)
2
(Circle)
3
(Circle)

Step 3. Add up the areas of the shapes that make up the cylinder.

The surface area of this cylinder is .
Awesome! If you’d like to practice additional problems finding the surface area of cylinders, expand the
Practice
below before closing out this lesson! ⚡
PRACTICE
Surface Area of Cylinders

Practice: Surface Area of Cylinders

Question 1 of 5: Find the surface area of this cylinder:

Step 1. Unwrap the cylinder.

Step 2. Calculate the area of each shape in the net.

Since the net is made up of one rectangle and two identical circles, we only need to find the area of the rectangle and one of the circles.
ShapeArea
1
(Rectangle)
2
(Circle)
3
(Circle)
The same area as the area of shape

Step 3. Add up the area of all the shapes that make up the cylinder.

Awesome job! The surface area of the cylinder is .

CONCLUSION
Nice work, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?
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