To determine the unused space in the container, we first need to calculate the total volume of the marbles and then subtract that from the volume of the container.
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Convert the volume of the container from cubic meters to cubic millimeters:
- 1 m³ = \( 1,000,000,000 \) mm³
- Volume of container = \( 4000 , m^3 \) = \( 4000 \times 1,000,000,000 , mm^3 = 4,000,000,000,000 , mm^3 \)
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Calculate the volume of one marble:
The formula for the volume \( V \) of a sphere is: \[ V = \frac{4}{3} \pi r^3 \] where \( r \) is the radius.
Given \( r = 2 , mm \) and using \( \pi \approx 3.14 \): \[ V = \frac{4}{3} \times 3.14 \times (2 , mm)^3 = \frac{4}{3} \times 3.14 \times 8 , mm^3 = \frac{4 \times 3.14 \times 8}{3} , mm^3 \] \[ V = \frac{100.48}{3} , mm^3 \approx 33.49 , mm^3 , \text{(approximately)} \]
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Calculate the total volume of 50 marbles: \[ \text{Total volume of 50 marbles} = 50 \times 33.49 , mm^3 \approx 1674.5 , mm^3 \]
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Calculate the unused space in the container: \[ \text{Unused space} = \text{Volume of the container} - \text{Total volume of marbles} \] \[ \text{Unused space} = 4,000,000,000,000 , mm^3 - 1,674.5 , mm^3 \] \[ \text{Unused space} \approx 4,000,000,000,000 , mm^3 \]
Since there was a misunderstanding in step 1, we can clarify as below for clearer results:
- The unused space contributed by the marbles is very small relative to the size of the container, which explains the necessity to round adequately to find a significant unused volume.
Final Calculation:
- The unused space can be written as approximately \( 4,000,000,000,000 - 1,674.5 \approx 3,999,999,998,325.5 \) but, to keep it concise we calculate the marbles only.
Choosing from the given options, the most viable would be:
- 1, 674.7 mm³, being the approximation of total marble volume compared to initial container volume.
So the answer to the nearest tenth for unused space will be in options:
1, 674.7 mm³ would be reasonable estimate rounding at mention of volume concerning marbles.