Body diagonal

The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal?

Correct answer:

u =  6 cm

Step-by-step explanation:

$$\begin{gathered} V=a^{2}c=32 \\ 4\cdot a\cdot c=2a^2 \\ 2c=a \\ 4c^{2}c=32 \\ {c}^3=8 \\ c=\sqrt[3]{8}=2 \\ a=2\cdot c=2\cdot 2=4 \\ u=\sqrt{a^2+a^2+c^2}=\sqrt{4^2+4^2+2^2}=6\text{ cm} \end{gathered}$$

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