This may be a great way to teach your children or younger sibling.
Step 1: What Is a Cylinder?
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
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
It looks like a cylinder, doesn't it?
Step 4: Taking It All Apart
Step 5: Area of the Parts
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?