3 A cylindrical metal tin of radius \(r \mathrm {~cm}\) is closed at both ends. It has a volume of \(16000 \pi \mathrm {~cm} ^ { 3 }\).
- Show that its total surface area, \(A \mathrm {~cm} ^ { 2 }\), is given by \(A = 2 \pi r ^ { 2 } + 32000 \pi r ^ { - 1 }\).
- Use calculus to determine the minimum total surface area of the tin. You should justify that it is a minimum.