Relating math formulae to the physical world

I always puzzled over the formula to calculate the area of a cylinder. Then I played with paper, tape, and string to figure out the relationship the formula had to the cylinder and to the physical world. This is what I found -

A cylinder transforms into a flat rectangle (L x W) = (W x L) when it's cut away from the top and bottom circles, and cut along its length. Then it's a matter of calculating the area of the 2 circles, and the side (now a flat rectangle) of the cylinder.

Area af a Cylinder

= (2 x (π RxR = area of a circle))
+ ( (W = 2π R where R is the radius of the cylinder, a circle)
x  (L = the length of the cylinder) )

Eureka!

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