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.
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?
1 answer
1 answer