The volume of a container measures 4000 mm to the third power 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 10th.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
First, let's calculate the volume of one marble.
V = (4/3) * 3.14 * 2^3
V ≈ 33.493
Now, let's calculate the total volume of all the marbles.
Total volume of marbles = 50 * 33.493
Total volume of marbles = 1674.65
To find the unused space in the box, we subtract the total volume of the marbles from the volume of the container.
Unused space = 4000 - 1674.65
Unused space ≈ 2325.35
Therefore, the amount of space in the box that is unused is approximately 2325.4 mm^3.