Height of Water After Submerging Rectangular Prism

A cylindrical container with a radius of 5 cm and height of 12 cm is filled with water. A rectangular prism is submerged in the water. The rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 8 cm. When the prism is submerged, it displaces a volume of water equal to its own volume. Determine the height of the water in the cylindrical container after the rectangular prism is submerged. Round your answer to the nearest hundredth.

Use the formula for the volume of a cylinder: $$V = \pi r^2 h$$ and the volume of a rectangular prism: $$V = l \cdot w \cdot h$$ where $r$ is the radius, $h$ is the height, $l$ is the length, and $w$ is the width.