Body diagonal

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

Result

V =  81189.882 dm3

Solution:

u=75 dm a=u/3=75/3≐25 3 dm≐43.3013 dm  V=a3=43.30133≐81189.8816≐81189.882 dm3u=75 \ \text{dm} \ \\ a=u/\sqrt{ 3 }=75/\sqrt{ 3 } \doteq 25 \ \sqrt{ 3 } \ \text{dm} \doteq 43.3013 \ \text{dm} \ \\ \ \\ V=a^3=43.3013^3 \doteq 81189.8816 \doteq 81189.882 \ \text{dm}^3

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