# Center of the cube

The Center of the cube has a distance 16 cm from each vertex.

Calculate the volume V and surface area S of the cube.

Correct result:

V =  6306.2 cm3
S =  2048 cm2

#### Solution:

$u = 2 \cdot 16 = 32 \ cm \ \\ u = \sqrt{3} a \ \\ a = \dfrac{u}{\sqrt{3}} = \dfrac{ 32 }{\sqrt{3}} = 18.475 \ cm \ \\ V = a^3 = 18.475^3 = 6306.2 \ \text{cm}^3$
$S = 6a^2 = 6\cdot 18.475^2 = 2048 \ \text{cm}^2$

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