Body diagonal

Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.

Correct answer:

V =  81189.8816 dm³

Step-by-step explanation:

$$\begin{gathered} u=75\text{ dm } \\ a=u\mathrm{/}\sqrt{3}=75\mathrm{/}\sqrt{3}=25\sqrt{3}\text{ dm}\doteq 43.3013\text{ dm } \\ V=a^3=43.3013^3=81189.8816{\text{dm}}^3=8.119\cdot 10^4{\text{dm}}^3 \end{gathered}$$

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