An open-topped cylindrical pot is to have volume 125 cm3. Determine the minimum possible amount of material used in making this pot? Neglect the thickness of the material as well as possible wastage. Give your answer accurate to 2 decimal places.

Answer 1

let the radius of the can be r cm
and its height be h cm

V= πr^2h
125 = π(r^2)h
h = 125/(πr^2)

surface area = bottom + rectangle
= πr^2 + 2πrh
= πr^2 + 2πr(125/(πr^2)
= πr^2 + 250/r

d(surface area)/dr = 2πr - 250/r^2
= 0 for a min of surface area

2πr = 250/(r^2)
r^3 = 125/π
r = 3.414

put that back into surface area = ...

( I got appr. 109.84)