Body diagonal

Calculate the volume and surface of the cube if the body diagonal measures 10 dm.

Correct result:

V =  192.4501 dm³
S =  200 dm²

Solution:

$$\begin{gathered} u=10\text{ dm } \\ a=u\mathrm{/}\sqrt{3}=10\mathrm{/}\sqrt{3}\doteq 5.7735\text{ dm } \\ V=a^3=5.7735^3=192.4501{\text{dm}}^3 \end{gathered}$$

$S=6\cdot a^2=6\cdot 5.7735^2=200{\text{dm}}^2$

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