Sphere of radius

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We have a sphere of radius R, with a rope of length 2 pi R around its
circumference; then we add L units to that circumference. What is the
new radius of the rope? The new circumference is (2 pi R + L); the new
radius is that divided by 2 pi, or R + L/(2 pi). This means that the
radius is increased by L/(2 pi), which is independent of R.

This seems a little less surprising, perhaps, than if we solved it with specific
numbers, since we don't have a specific unexpectedly large number to
reject outright; we're forced to look at the algebra. more help on online math forum;
But we can still question the algebra once we see what it tells us.

The next step, of course, is to check the answer: plug in actual numbers for R and L,
solve for the change in R, and then add that to R to find what the new
circumference will be. It will be L more than the original, showing
that as long as we accept 2 pi R, our answer is right. read more on math forum.