Surface and volume - cube

Find the surface and volume of a cube whose wall diagonal is 5 cm long.

Correct answer:

S =  75 cm²
V =  44.1942 cm³

Step-by-step explanation:

$$\begin{gathered} u=5\text{ cm } \\ {u}^2=a^2+a^2=2a^2 \\ a=u\mathrm{/}\sqrt{2}=5\mathrm{/}\sqrt{2}\doteq 3.5355\text{ cm } \\ S=6\cdot a^2=6\cdot 3.5355^2=75{\text{cm}}^2 \end{gathered}$$

$V=a^3=3.5355^3=44.1942{\text{cm}}^3$

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