Lesson AREA of a cylinder

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It is very easy to derive a formula for the area of a cylinder with radius r and height h.

Think about how you would make a cylinder out of paper. You would need two circles for both sides of the cylinder. Each of thee sides would have radius r and, therefore, area pi%2Ar%5E2. Since you have two sides, their combined area would be twice that, that is 2pi%2Ar%5E2.

Now, to make the side of the cylinder, you would need to cut a rectangle that is the right length to wrap over the base and top circles, with the other dimension being the height of the cylinder. When you make a tube out of that piece, that tube will be the sides of the rectangle. The length necessary to just wrap around the base is the perimeter of the circle of the base. That perimeter is 2*pi*r.

That means that we have a rectangle 2*pi*r by h. The area of that rectangle is tyhe multiple of the dimensions of the sides, or 2*pi*r*h.

The total area is the sum of areas of bases and the sides, or 2pi%2Ar%5E2+%2B+2pi%2Ar%2Ah.
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