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Solutions: 0

V/π = VThe surface area of each hemisphere is S_{sphere}/π + V_{cylinder}/π = (4/3)R^{3}+ R^{2}h

SThe lateral surface area of the cylinder is S_{hemi}/π = 2R^{2}

SThe above three quantities are integers by convention. We can write_{cyl}/π = 2Rh

so R is rational. The equability assumption is

V = 2Swhich reduces to_{hemi}+ S_{cyl},

3h(R - 2) = 4R(3 - R)Incidentally, h is rational since it can be written as the quotient of rationals if R ≠ 2. Since h > 0 and R > 0, R - 2 and 3 - R must have the same sign, so

2 < R < 3By writing the fractionS

_{hemi}/π = 2R^{2}∈ {9,10,11,12,13,14,15,16,17}4R

^{2}∈ {18,20,22,24,26,28,30,32,34}

we can see that no feasible value of 4R

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