The volume of a container measures 4,000 mm ^3 and contains 50 marbles. Each marble has a radius of 2 mm. Use 3.14 as an approximation for pi. How much space in the box is unused? Round your answer to the nearest tenth.
The volume of each marble can be calculated using the formula for the volume of a sphere, which is $\frac{4}{3}\pi r^3$. Using the given radius of 2 mm and approximating $\pi$ to 3.14, we have:
\[
\frac{4}{3} \times 3.14 \times 2^3 \approx 33.49
\]
Therefore, the volume of 50 marbles is $50 \times 33.49 = 1674.5$ mm$^3$.
The unused space in the box is the total volume of the container minus the volume of the marbles, which is $4000 - 1674.5 = 2325.5$ mm$^3$.
Rounding to the nearest tenth, the unused space in the box is approximately $\boxed{2325.5}$ mm$^3$.