The can should be 12.4 cm tall with a radius of 6.2 cm.

Volume: V = 2*pi*R^2*h
Surface Area: A = 2*pi*R*h + 2*pi*R^2

V = 1500cc = 2*pi*R^2*h --> h = 1500/(2*pi*R^2)

To minimize the area, take derivatives and set them to zero.

dA/dh = 0 = 2*pi*R = 0 --> implies that R = 0, an invalid solution
dA/dR = 0 = d/dR{2*pi*R*h + 2*pi*R^2}
        0 = d/dR{2*pi*R(1500/(pi*R^2)) + 2*pi*R^2
        0 = d/dR{3000/(pi*R) + 2*pi*R^2
        0 = -3000/(pi*R^2) + 4*pi*R 
        

Solve this for R and you get 6.2 cm. Plug this back into the volume equation and solving for h give you 12.4 cm