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 f pi. How much space in the box is unused? Round your answer to the nearest tenth. (1 point)
33.5m * m ^ 3
0.674 * 0.7m * m ^ 3
O2 ,325.3 mm^ 3
3.9m * 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.
Given that the radius of each marble is 2 mm, we can plug this value into the formula:
V = (4/3) * 3.14 * (2 mm)^3
V = (4/3) * 3.14 * 8 mm^3
Simplifying the equation:
V = 33.493 mm^3
Since there are 50 marbles in the container, the total volume of all the marbles is:
50 * 33.493 mm^3 = 1674.65 mm^3
Now, to convert this volume to cubic meters, we divide by 1,000,000 (since there are 1,000,000 mm^3 in a cubic meter):
1674.65 mm^3 ÷ 1,000,000 = 0.00167465 m^3
Therefore, the volume of unused space in the box is:
0.00167465 m^3
Rounded to the nearest tenth, the answer is:
0.0 m^3 (since the unused space is negligible)