The volume of a container measures 4,000 mm3 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) Responses 33.5 mm3 33.5 mm cubed 1,674.7 mm3 1,674.7 mm cubed 2,325.3 mm3 2,325.3 mm cubed 3,900 mm3
The volume of each marble can be calculated using the formula for the volume of a sphere:
V = (4/3) * π * r^3
V = (4/3) * 3.14 * (2 mm)^3
V ≈ 33.49 mm^3
Therefore, the total volume occupied by the marbles is 50 marbles * 33.49 mm^3/marble ≈ 1674.5 mm^3.
To find the unused space in the box, we subtract the volume occupied by the marbles from the total volume of the container:
Unused space = Total volume of the container - Volume occupied by marbles
Unused space = 4000 mm^3 - 1674.5 mm^3
Unused space ≈ 2325.5 mm^3
Rounding to the nearest tenth, the unused space in the box is approximately 2325.3 mm^3.
Therefore, the correct answer is 2325.3 mm^3.