Cuboid diagonals

The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.

Correct result:

V =  12000 cm³
S =  3400 dm²
u₁ =  25 dm
u₂ =  42.72 dm
u₃ =  44.7214 dm
s =  47.1699 dm

Solution:

$$\begin{gathered} a=15\text{ cm } \\ b=20\text{ cm } \\ c=40\text{ cm } \\ V=a\cdot b\cdot c=15\cdot 20\cdot 40=12000{\text{cm}}^3 \end{gathered}$$

$S=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (15\cdot 20+20\cdot 40+40\cdot 15)=3400{\text{dm}}^2$

$u_1=\sqrt{a^2+b^2}=\sqrt{15^2+20^2}=25\text{ dm}$

$u_2=\sqrt{a^2+c^2}=\sqrt{15^2+40^2}=5\sqrt{73}=42.72\text{ dm}$

$u_3=\sqrt{b^2+c^2}=\sqrt{20^2+40^2}=20\sqrt{5}=44.7214\text{ dm}$

$s=\sqrt{a^2+b^2+c^2}=\sqrt{15^2+20^2+40^2}=5\sqrt{89}=47.1699\text{ dm}$

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