A straight cylinder of height h=1 cm has its basis on the xy plane defined by: \[x^2 + y^2 - 2x - 4y + 4 \leq 0\]

Another plane containing the line \[y - x = 0\] and parallel to the cylinder axis, cuts it in two solids. Calculate the surface area of the smaller solid.

Use, if necessary: \[π=3, \sqrt{2}=1.4, \sqrt{3}=1.7, \sqrt{5}=2.2\]

This was slightly modified from a question of ITA-Brazil 2013-2014 Entrance Exam

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