The cost of producing an ordinary cylindrical tin can is determined by the materials used for the wall and the end points. If the end pieces are twice as expensive per square cm as the wall, find the dimensions (to the nearest millimeter) to make a 1000 cm^3 can at minimal cost.

Here is my work.. but does not lead to correct answer

End pieces are 2k/cm

Wall pieces are k/cm

Min cost

=2k(2pi(r^2))+k(2pi)(h)

=2k(2pi)(r^2)+k(2pi(1000/(pi(r^2))

=4pi(k)(r^2)+2000k(r^-2)

C'(r)=8pi(k)(r)-4000k(r^-3)

C'(r)=0 when r=aprox 1.99

However, their answer is

r=43 mm and height = 172 mm.