# Body diagonal

Calculate the volume and surface of the cube if the body diagonal measures 10 dm.

Result

V =  192.45 dm3
S =  200 dm2

#### Solution:

$u=10 \ \text{dm} \ \\ a=u / \sqrt{ 3 }=10 / \sqrt{ 3 } \doteq 5.7735 \ \text{dm} \ \\ \ \\ V=a^3=5.7735^3 \doteq 192.4501 \doteq 192.45 \ \text{dm}^3$
$S=6 \cdot \ a^2=6 \cdot \ 5.7735^2=200 \ \text{dm}^2$

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