The volume of a container measures 0m * m ^ 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 point) 1, 674.7m * m ^ 3; 33.5m * m ^ 3; 3, 900m * m ^ 3; 1.325 * 0.3m * m ^ 3
To calculate the volume of the marbles, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Where V is the volume, π is approximately 3.14, and r is the radius.
Let's calculate the volume of one marble:
V = (4/3) * 3.14 * (0.002m)^3
= (4/3) * 3.14 * 0.000000008m^3
≈ 3.35 x 10^-8 m^3
Next, to find the total volume of the marbles, we need to multiply the volume of one marble by the number of marbles:
Total volume of marbles = (3.35 x 10^-8 m^3) * 50
= 1.675 x 10^-6 m^3
Finally, to find the space unused in the box, we subtract the volume of the marbles from the volume of the container:
Unused space = (0m * m^3) - (1.675 x 10^-6 m^3)
≈ -1.675 x 10^-6 m^3
Since the result is negative, it means that the marbles are taking up more volume than the container can hold. Therefore, the answer is None of the above.