A metal storage tank with volume 5m^3 is to be constructed in the shape of a right circular cylinder surmounted by a hemisphere. What dimensions will require the least amount of metal? (Hint: for atleast amount of metal, the surface area should be a min)

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A metal storage tank with volume 5m^3 is to be constructed in the shape of a right circular cylinder surmounted by a hemisphere. What dimensions will require the least amount of metal? (Hint: for atleast amount of metal, the surface area should be a min)

Mathematics
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so v=(pi)r^2 * h + (2/3)(pi)r^2?
surface area = (pi)r^2 + 2(pi)rh + 2(pi)r^2
for volume plug in 5 for v and calculate h in terms of r

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[5 - (2/3)(pi)r^2] / (pi)r^2 = h
5/(pi)r^2 - (2/3) = h
surface area = 3(pi)r^2 + 2(pi)rh plug in for h 3(pi)r^2 + 2(pi)r[5/(pi)r^2 - (2/3)] = 3(pi)r^2 + 10/(pi)r - 4(pi)r/3
thanks a bunch!

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