The volume of a container measures 4,000 mm^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?
First, we need to calculate the total volume occupied by the marbles in the container.
The volume of each marble can be calculated using the formula for the volume of a sphere: V = (4/3) * π * r^3, where r is the radius of the marble.
V = (4/3) * 3.14 * 2^3
V = (4/3) * 3.14 * 8
V = 33.4933 mm^3
The total volume occupied by the marbles can be calculated by multiplying the volume of one marble by the total number of marbles:
Total volume occupied by marbles = 33.4933 mm^3/marble * 50 marbles
Total volume occupied by marbles = 1674.665 mm^3
To find the unused space in the box, subtract the total volume occupied by the marbles from the total volume of the container:
Unused space = Total volume of the container - Total volume occupied by marbles
Unused space = 4000 mm^3 - 1674.665 mm^3
Unused space = 2325.335 mm^3
Therefore, there is approximately 2325.335 mm^3 of unused space in the box.