Body diagonal - cube

Calculate the surface and cube volume with body diagonal 15 cm long.

Correct answer:

S =  450 cm²
V =  649.5191 cm³

Step-by-step explanation:

$$\begin{gathered} u=15\text{ cm } \\ a=u\mathrm{/}\sqrt{3}=15\mathrm{/}\sqrt{3}=5\sqrt{3}\text{ cm}\doteq 8.6603\text{ cm } \\ S=6\cdot a^2=6\cdot 8.6603^2=450{\text{cm}}^2 \end{gathered}$$

$V=a^3=8.6603^3=375\sqrt{3}=649.5191{\text{cm}}^3$

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