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v = πr^2h = 5, so
h = 5/(Ï€r^2)
a = 2Ï€r^2 + 2Ï€rh
= 2Ï€r^2 + 10/r
da/dr = 4Ï€r - 10/r^2
da/dr=0 when 4Ï€r^3=10
r = ∛(5/(2π))
h = 5/(πr^2) = 5/(π(5/(2π))^(2/3)) = ∛(20/π)
since 3 > 2r > h, it works.