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.

Correct 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}

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators

Do you know the volume and unit volume, and want to convert volume units?
The Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

algebra

arithmetic

solid geometry

planimetrics

goniometry and trigonometry

Units of physical quantities

Grade of the word problem

We encourage you to watch this tutorial video on this math problem: video1 video2