Question

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)

Answer 1

so v=(pi)r^2 * h + (2/3)(pi)r^2?

Answer 2

surface area = (pi)r^2 + 2(pi)rh + 2(pi)r^2

Answer 3

for volume plug in 5 for v and calculate h in terms of r

Answer 4

[5 - (2/3)(pi)r^2] / (pi)r^2 = h

Answer 5

5/(pi)r^2 - (2/3) = h

Answer 6

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

Answer 7

thanks a bunch!