# 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:

$u=75 \ \text{dm} \ \\ a=u/\sqrt{ 3 }=75/\sqrt{ 3 } \doteq 25 \ \sqrt{ 3 } \ \text{dm} \doteq 43.3013 \ \text{dm} \ \\ \ \\ V=a^3=43.3013^3 \doteq 81189.8816 \doteq 81189.882 \ \text{dm}^3$

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