Cube diagonals

Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.

Correct answer:

V =  1939453.4995 cm³
S =  93312 cm²

Step-by-step explanation:

$$\begin{gathered} u=216 \\ a=u\mathrm{/}\sqrt{3}=216\mathrm{/}\sqrt{3}=72\sqrt{3}\doteq 124.7077 \\ V=a^3=124.7077^3=1939453.4995{\text{cm}}^3=1.939\cdot 10^6{\text{cm}}^3 \end{gathered}$$

$S=6\cdot a^2=6\cdot 124.7077^2=93312{\text{cm}}^2$

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