# Cube diagonals

Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.

Correct result:

V =  1939453.499 cm3
S =  93312 cm2

#### Solution:

$u=216 \ \\ a=u /\sqrt{ 3 }=216 /\sqrt{ 3 } \doteq 72 \ \sqrt{ 3 } \doteq 124.7077 \ \\ V=a^3=124.7077^3=1939453.499 \ \text{cm}^3=1.939453\cdot 10^{ 6 } \ \text{cm}^3$
$S=6 \cdot \ a^2=6 \cdot \ 124.7077^2=93312 \ \text{cm}^2$

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