Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.

Correct answer:

a =  9 cm
u₁ =  12.7279 cm
u₂ =  15.5885 cm

Step-by-step explanation:

$$\begin{gathered} S_1=81{\text{cm}}^2 \\ a=\sqrt{S_1}=\sqrt{81}=9\text{ cm} \end{gathered}$$

$$\begin{gathered} u_1^2=a^2+a^2=2a^2 \\ {u}_1=\sqrt{2}\cdot a=\sqrt{2}\cdot 9=9\sqrt{2}=12.7279\text{ cm} \end{gathered}$$

$$\begin{gathered} u_2^2=a^2+a^2+a^2=3a^2 \\ {u}_2=\sqrt{3}\cdot a=\sqrt{3}\cdot 9=9\sqrt{3}=15.5885\text{ cm} \end{gathered}$$

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Math student

very nice this calculator thnk

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