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.

1 answer

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$^3$.