6. Suppose the axial section of an inverted conical container is an equilateral triangle. Water is poured into this container, and a solid sphere with radius $r$ is placed inside. If the sphere is submerged in the water and is tangent to the container walls and the water surface, then the height of the water level after the sphere is removed is ( ).
(A) $r$
(B) $2 r$
(C) $\sqrt[3]{12} r$
(D) $\sqrt[3]{15} r$
6. D.

Figure 3 shows the axial section $P A B$ of a cone, with the center of the sphere being O. It is easy to see that,
$$
\begin{array}{c}
P C=O C+P O \\
=r+2 r=3 r, \\
A C=\sqrt{3} r, \\
V_{P A B}=\frac{1}{3} \pi(\sqrt{3} r)^{2} \cdot 3 r=3 \pi r^{3} .
\end{array}
$$

Let the water surface after removing the sphere be $E F$. Then,
$$
V_{P E F}=3 \pi r^{3}-\frac{4}{3} \pi r^{3}=\frac{5}{3} \pi r^{3} \text {. }
$$

Since $\frac{V_{P E F}}{V_{P A B}}=\frac{h^{3}}{P C^{3}}$, we have,
$$
h^{3}=15 r^{3} \Rightarrow h=\sqrt[3]{15} r
$$