Sphere cut

A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the volume of the segment. What is the distance of the cutting plane from the center of the sphere?

Correct result:

x =  0

Solution:

$$\begin{gathered} r=1 \\ x=V_1={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 1^3\doteq 4.1888=0 \end{gathered}$$

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