Cube diagonals

Determine the length of the body and wall diagonals of the cube, the volume of which is equal to 0.343 decimetres. Also, calculate its surface.

Final Answer:

u₁ =  0.9899 dm
u₂ =  1.2124 dm
S =  2.94 dm²

Step-by-step explanation:

$$\begin{gathered} V=0.343 \\ a=\sqrt[3]{V}=\sqrt[3]{0.343}=\frac{7}{10}=0.7 \\ {u}_1=\sqrt{2}\cdot a=\sqrt{2}\cdot 0.7=0.9899\text{dm} \end{gathered}$$

$u_2=\sqrt{3}\cdot a=\sqrt{3}\cdot 0.7=1.2124\text{dm}$

$S=6\cdot a^2=6\cdot 0.7^2=2.94{\text{dm}}^2$

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