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We know that V <code> (4/3)'''pi'''r^3 and A </code> 4'''pi'''r^2.
We need to find out how much V increases if A increases by 1 m^2.

  dV / dr = 4 ''' pi ''' r^2
  dA / dr = 8 ''' pi ''' r
  dV / dA = (dV / dr) / (dA / dr)
	  = (4 ''' pi ''' r^2) / (8 ''' pi ''' r)
	  = r/2
          = 3,250,000 m

If the area of the cover is increased by 1 square meter,
then the volume it contains is increased by about 3.25 million cubic meters.

We seem to be getting a lot of mileage out of such a small square of cotton.
However, the new cover would not be very high above the surface of the
planet -- about 6 nanometers (calculate dr/dA).
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