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V = a^3
SA = 6a^2
f = a\sqrt{2}
$ \text{From Volume: } a = \sqrt[3]{V} $ $ \text{From Surface Area: } a = \sqrt{SA / 6} $ $ \text{From Face Diagonal: } a = f / \sqrt{2} $ $ \text{From Space Diagonal: } a = d / \sqrt{3} $
$ a = \sqrt{SA / 6} = \sqrt{150 / 6} = \sqrt{25} = 5 \text{ ft} $
$ V = a^3 = 5^3 = 125 \text{ ft}^3 $
$ d = a\sqrt{3} = 5 \times 1.732... \approx 8.66 \text{ ft} $