92 A container in the shape of an equilateral circular cone is filled with water, the water surface bisects the height, after sealing this container and inverting it (base facing up), the height of the water surface is $\qquad$ of the cone's height.
$921-\frac{\sqrt[3]{7}}{2}$. The water occupies the volume of the cone $\left(\frac{1}{2}\right)^{3}=\frac{1}{8}$. After inversion, the empty part occupies $\frac{7}{8}$ of the cone, the height of the water surface is
$$
1-\sqrt[3]{\frac{7}{8}}=1-\frac{\sqrt[3]{7}}{2} .
$$