To find the unused space in the container, we first need to calculate the volume occupied by the marbles and then subtract that from the total volume of the container.
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Calculate the volume of a single marble:
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the marble.
Given that the radius \( r = 2 \) mm and using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (2)^3 \]
\[ V = \frac{4}{3} \times 3.14 \times 8 \]
\[ V = \frac{4 \times 3.14 \times 8}{3} \]
\[ V = \frac{100.48}{3} \approx 33.49 \text{ mm}^3 \]
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Calculate the total volume occupied by 50 marbles:
The total volume occupied by the marbles is:
\[ \text{Total volume} = 50 \times 33.49 \text{ mm}^3 = 1674.5 \text{ mm}^3 \]
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Calculate the unused space in the container:
The total volume of the container is 4000 mm³. To find the unused space:
\[ \text{Unused space} = \text{Total volume of the container} - \text{Total volume occupied by marbles} \]
\[ \text{Unused space} = 4000 \text{ mm}^3 - 1674.5 \text{ mm}^3 = 2325.5 \text{ mm}^3 \]
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Round to the nearest tenth:
Rounding \( 2325.5 \) mm³ gives us 2325.5 mm³.
Thus, the unused space in the box is approximately 2325.5 mm³. However, since that option does not exactly match the given choices, we find that 2,325.3 mm³ is the closest option available.
Answer: 2,325.3 mm³