Drum tight containers is designing an open-top, square-based, rectangular box that will have a volume of 1098.5 inches cubed. what dimensions will minimize surface area? what is the minimum surface area?

Area = s^2 + 4sh
For minimum dA/ds = 2s + 4h = 0
s = -2h

But s^2h = 1098.5
(-2h)^2 h = 1098.5
4h^3 = 1098.5
h^3 = 1098.5/4 = 274.625
h = cube roof of 274.625 = 6.5 inches

Thus, s^2(6.5) = 1098.5
s^2 = 169
s = sqrt(169) = 13 inches

Therefore, to minimize the surface area, the square base should have sides of 13 inches while the height should be 6.5 inches.
Surface area = (13)^2 + 4(13 x 6.5) = 169 + 338 = 507 inches

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