To find the unused space in the container, we first need to calculate the volume of a single marble and then multiply it by the number of marbles to find the total volume of all the marbles. Finally, we'll subtract the total volume of the marbles from the 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. Given that the radius of each marble is 2 mm and using \( \pi \approx 3.14 \): \[ V = \frac{4}{3} \times 3.14 \times (2)^3 \] \[ V = \frac{4}{3} \times 3.14 \times 8 \] \[ V = \frac{4}{3} \times 25.12 \] \[ V \approx \frac{100.48}{3} \approx 33.49 \text{ mm}^3 \]
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Calculate the total volume of 50 marbles: \[ \text{Total volume of marbles} = 50 \times 33.49 \approx 1674.5 \text{ mm}^3 \]
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Calculate the unused space in the container: The volume of the container is 4,000 mm³. Therefore, \[ \text{Unused space} = \text{Volume of container} - \text{Total volume of marbles} \] \[ \text{Unused space} = 4000 - 1674.5 \approx 2325.5 \text{ mm}^3 \]
Rounding this to the nearest tenth, we get 2325.5 mm³.
Therefore, the correct response is: 2,325.3 mm³.