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? Round your answer to the nearest tenth.(1 point) Responses 3,900 mm^3 3,900 mm cubed 1,674.7 mm^3 1,674.7 mm cubed 33.5 mm3 33.5 mm cubed 2,325.3 mm^3
To find the total volume occupied by the 50 marbles, we multiply the volume of each marble by the number of marbles:
Volume of each marble = (4/3) * pi * radius^3
Volume of each marble = (4/3) * 3.14 * 2^3
Volume of each marble = (4/3) * 3.14 * 8
Volume of each marble = 33.49 mm^3 (rounded to the nearest hundredth)
Total volume of all marbles = 50 * 33.49
Total volume of all marbles = 1,674.5 mm^3
Now, we subtract the total volume of all the marbles from the volume of the container to find the unused space:
Unused space = 4,000 - 1,674.5
Unused space = 2,325.5 mm^3
Therefore, the unused space in the box is 2,325.5 mm^3, rounded to the nearest tenth. The closest answer choice is 2,325.3 mm^3.