A rectangle storage container has a volume of 10 meters cubed and no top. The length is twice the width, the base material costs $10 per meter cubed and the side material costs $6 per meter cubed. Calculate the dimensions of the box that minimize total cost of materials.

$\displaystyle

V = lwh = 10

$

$\displaystyle 2l = w$

$\displaystyle V = 2l^2h$

$\displaystyle SA = (10)(2l^2) + 4[6(lh)]$

$\displaystyle SA = 20l^2 + 24lh$

$\displaystyle

H = 5/l^2

$

$\displaystyle SA = 20l^2 + 120/l$

$\displaystyle SA' = 40l - 120/l^2 = 0$

l = cubed root of 3?

is this much correct?