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→The section of a cylinder as a squared circle
If the external surface of the straight side of the cylinder only is opened up and laid flat, its area can be determined by measuring the four sides of the resultant rectangle with a straightedge. The lengths of the top edge and the bottom edge only of the opened and flattened area of the straight sides of the cylinder are identical to the circumference of the circular ends, each length taken and divided by four and rearranged as four equal straight sides of a square, the area of the resultant square determined for one end of the cylinder is then multiplied by two for both ends, and the resulting combined area of the two ends added to the area of the opened and flattened straight side of the cylinder, give the area of the squared-off circular surface of the single cylindrical section with both round ends, the area of this one single squared circle object determined by straightedge measurement (6).
If the external surface of the straight side of the cylinder only is opened up and laid flat, its area can be determined by measuring the four sides of the resultant rectangle with a straightedge. The lengths of the top edge and the bottom edge only of the opened and flattened area of the straight sides of the cylinder are identical to the circumference of the circular ends, each length taken and divided by four and rearranged as four equal straight sides of a square, the area of the resultant square determined for one end of the cylinder is then multiplied by two for both ends, and the resulting combined area of the two ends added to the area of the opened and flattened straight side of the cylinder, give the area of the squared-off circular surface of the single cylindrical section with both round ends, the area of this one single squared circle object determined by straightedge measurement (6).
This simple solution with basic arithmetic and practical [[common sense]] elegantly does away with any need for the exact value of the transcendent number '''<big><big>π</big></big>''' ''pi'' and the [[Cylinder|formula]] '''<math> S= 2\pi r^2 + 2\pi r h \ .</math>''']]
This simple solution using basic arithmetic and practical [[common sense]] elegantly does away with any need for the exact value of the transcendent number '''<big><big>π</big></big>''' ''pi'' and the [[Cylinder|formula]] '''<math> S= 2\pi r^2 + 2\pi r h \ .</math>'''