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The surface area of a cylinder is 2 pi r2 + 2 pi rh, where r is the radius of the circular top or bottom of the cylinder and h is the height of the cylinder.

Think of a can of soup, and imagine having to cover the entire surface area of that can with paper. You could wrap paper around the outside of the can. Think about the label on a can of soup. What would it look like if you peeled it off in one piece? It would be a rectangle of paper, right? How do you measure the area of a rectangle? Multiply the length and the width. The width of that rectangle would be the height of the can, h. The length of that rectangle would be the circumference of the circle that represents the outside edge of the top or bottom of the can. So there's part of the answer. The area of the outside of the cylinder would be the circumference of the top or bottom x the height. Since the formula for circumference is 2 pi r, the area is 2 pi rh.

You're not done yet! You need to calculate the area of the top and the bottom of the cylinder, too. That's the easy part. Just figure out the area of the circle: pi r 2. The only trick is that since you have a top and a bottom to cover, you have to multiply that quantity by 2.

So there's your final answer: 2 pi r2 + 2 pi rh!

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