Such a figure with "width" x, "length" y and "height" z has volume xyz and surface area 2xy+ 2xz+ 2yz.
For this particular figure you are told that "Length of base is twice the width" so y= 2x.
Also, "the volumn is 1944cm^3" so so that .
(a) Since S= surface area= 2xy+ 2xz+ 2yz, y= 2x and , .
(b) One way to find the maximum value of a function is to find where its derivative is [/tex]0: S'= 8x- 5832/x^2= 0[/tex] so and and, finally, .