Calculate cuboid, diagonals

The volume of a cuboid with a square base is 64 cm³, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area.

Final Answer:

S = 86.7156 cm²

V = 64 cm^{3} α = 45^{\circ} V = a^{2} \cdot h tan α = h : u tan α = h : 2 a 2 \cdot a \cdot tan α = h V = a^{2} \cdot 2 \cdot a \cdot tan α V = 2 \cdot a^{3} \cdot tan α a = 3 \frac{V}{2 \cdot tan α} = 3 \frac{V}{2 \cdot tan 4 5 °} = 3 \frac{6 4}{2 \cdot tan 4 5 °} = 3 \frac{6 4}{2 \cdot 1} = 3.56359 cm h = 2 \cdot a \cdot tan α = 2 \cdot a \cdot tan 45 ° = 2 \cdot 3.5636 \cdot tan 45 ° = 2 \cdot 3.5636 \cdot 1 = 5.03968 cm S = 2 \cdot (a \cdot a + a \cdot h + a \cdot a) = 2 \cdot (3.5636 \cdot 3.5636 + 3.5636 \cdot 5.0397 + 3.5636 \cdot 3.5636) ≐ 86.7156 cm^{2} Verifying Solution: V_{2} = a^{2} \cdot h = 3.563 6^{2} \cdot 5.0397 = 64 cm^{3} u = 2 \cdot a = 2 \cdot 3.5636 ≐ 5.0397 cm α_{2} = \frac{1 8 0 °}{π} \cdot arctan (h / u) = \frac{1 8 0 °}{π} \cdot arctan (5.0397 / 5.0397) = 45^{\circ}

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