Friday, October 20, 2017

One way to visually understand why total surface area of a sphere doesn't double when its volume is doubled [COMPACTIDEA]

This explanation uses a cylinder, but if you think carefully, it applies to a sphere too, albeit it's tougher and more complicated to visualize it properly. Now, when the length of a cylinder is doubled, its volume doubles, but the original and new surface areas are as follows:
  1. SAW + SAE + SAE
  2. NSAW + SAE + SAE
Where SAW= surface area of wall, SAE= surface area of end, NSAW= new surface area of wall. When volume is doubled, NSAW= 2*SAW, but SAE remains SAE. So when volume is doubled, 2*SAE remains 2*SAE rather than becoming 4* SAE [size of caps at the ends remains the same], hence the total surface area is lower than twice.

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