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Why 2πrh?

 Why 2πrh?

 Do cylinders fascinate you? They do, for me. But then, one thing that I didn’t understand but was asked to memorize in my middle school was the formula for the Curved Surface Area of a cylinder. CSA = 2πrh, that’s what I knew. Never was I told why that particular combination of parameters that I well understood spitted out the area of the curved portion of the cylinder, for that matter. So, today, let’s ask ourselves: Why 2πrh?


On the left is a cylinder and on the right is the same cylinder with the shaded region being the part whose area needs to be calculated. Now, let’s take a pair of scissors, and cut the cylinder vertically starting from one point in the upper circumference and reaching another point, exactly down of the upper point, in the lower circumference. Then, we flatten the pieces cut against the back wall. You’ll soon see why we are doing this small piece of Origami-c exercise


As you do the folding as instructed, what you will get is a rectangle and the area of the rectangle would exactly be what we’d have been hunting for until now, that's exactly the Curved surface area if the cylinder were to be made again. The length of the rectangle is the perimeter of the circular base of the cylinder(2πr) [Why 2πr? in some other article], while the breadth would be equal to the height of the cylinder. And since the area of the rectangle is length times breadth, we have the CSA of a cylinder = 2πr . h = 2πrh. 
Interesting, isn't it? 


-Manoj Dhakal








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