



 
Hi there. If you take a finite strip of the cylinder and sphere, they are approximately equal  I don't think you are questioning this. The leap to exactness is due to taking a smaller and smaller strip height h_{c} and h_{s}. The smaller these are, the more exact the comparison becomes. When you use calculus, you make this height infinitely small, so the distortion (comparison of approximation to exact value) becomes infinitely small. It's a bit like comparing 0.9 to 1. That's approximately the same, but if we make it closer, then 0.99 is approximately 1, but certainly nearer than the first one. Similarly, 0.99999....repeating forever is infinitely close to 1, so we say it is equal to 1. Thus it is exact. Stephen La Rocque.>  


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