Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³.

Correct answer:

a =  3 cm
u₁ =  4.2426 cm
u₂ =  5.1962 cm

Step-by-step explanation:

$$\begin{gathered} V=27{\text{cm}}^3 \\ a=\sqrt[3]{V}=\sqrt[3]{27}=3\text{ cm} \end{gathered}$$

$u_1=\sqrt{2}\cdot a=\sqrt{2}\cdot 3=3\sqrt{2}=4.2426\text{ cm}$

$u_2=\sqrt{3}\cdot a=\sqrt{3}\cdot 3=3\sqrt{3}=5.1962\text{ cm}$

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