# Surface Area of a Cylinder

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Want to know how to figure out the area of a cylinder? Here's how! I prefer to learn hands-on, so I decided to make a cylinder instead of just writing equations.

This may be a great way to teach your children or younger sibling.

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## Step 1: What Is a Cylinder?

Before we jump into any math, we should find out what a cylinder is made of.

The answer is two circles and a rectangle.

But like many people, I am a visual learner - so lets actually make one!

First, find a circular object and trace two circles unto some colored paper. Cut them out. Fold them in half, and use a ruler to measer the crease (the diameter of a circle). To help me remember, I wrote the diameter on one of the circles.

## Step 2: The Rectangle

Next, we must make the rectangle that will be the "body" of the cylinder. The rectangle should wrap around the circle entirely. To find out how long the rectangle should be to wrap around the entire circle, we must find the circumference (the distance around) of the circle.

So, in the end, the circumference we got was 267mm. Measure 267mm on another sheet of colored paper and cut it out. While you're at it, measure the width of the paper, too. I wrote them down on the paper to help me remember.

## Step 3: Putting It Together

Tape the ends of the rectangle together. Then, tape the two circles two the ends of the tube you just made.

It looks like a cylinder, doesn't it?

## Step 4: Taking It All Apart

Now that we have a cylinder, and proved that it consists of two circles and a rectangle, lets cut it open again and lay the parts out flat.

## Step 5: Area of the Parts

So we have 3 parts to measure the area of. If we just add the areas of each of the 3 parts together, we have the area of the entire cylinder!

First, lets find the area of the circles. The equation is shown below. So in the end, we get 5674.5 as the area in millimeters squard for one circle. Multiply it by two and we get the area of both of the circles (11349 millimeters squared).

Now, we must find the area of the rectangle. An area of a rectangle is length times width. We found the width of the rectangle by finding the circumference of the circle (267mm). The length of the rectangle was 216mm, also the height of the cylinder. So, to put it more simply, the area of the rectangle is the height of the cylinder times the circumference of the circle.

267 times 216 is 57672 millimeters squared.

57672 plus 11349 is 69021 millimeters squared (or 6902 centimeters squared).

There it is, 6902 centimeters squared is the area of our cylinder!

So lets recap. The area of a cylinder is:
2(area of circle) + ((height of cylinder) times (circumference of circle))

## Step 6: What Now?

Try out your skills! Find a cylindrical object around the house and find the area of it.

Have fun!

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## 10 Discussions

Small problem there. 1 mm = 1/10 cm so 1 sq mm = 1/100 sq cm. This means 69021 sq mm = 690.21 sq cm = 0.069 sq m, which makes sense for a tuna can. You have 6902 sq cm = 0.69 sq m, which would be more like a coffee can or something similar.

Sigh. Maybe someday this will be written up in "regular people English" so that people like me (smart, but no math wiz) will be able to understand...

The formula for the dumb people like me that are too lazy to make this is 2(pi)r2 + 2(pi)rh