Three balls are packaged in a cylindrical container as shown. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 12 cm. With the balls still in the cylinder, what is the volume of the empty space in the cylinder? Round to the nearest cm cubed.

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.