Dividing a cube by 7

[math]\frac{1}{7}+\left(\frac{1}{7}\right)^2+\left(\frac{1}{7}\right)^3+\left(\frac{1}{7}\right)^4+\left(\frac{1}{7}\right)^5+...=[/math]

[math]\frac{1}{4}[/math] [math]\frac{1}{2}[/math] [math]\frac{2}{7}[/math] [math]\frac{1}{6}[/math] [math]\frac{3}{5}[/math]

Think how can you divide a cube into 7 equal parts, all of them with the same volume and surface as well.

Information: Dividing a cube by 7