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 1,674.7 mm3 1,674.7 mm cubed 33.5 mm3 33.5 mm cubed 3,900 mm3 3,900 mm cubed 2,325.3 mm3
The volume of a single marble can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3 = (4/3)(3.14)(2^3) = 33.49 mm^3
Total volume of all the marbles can be calculated by multiplying the volume of a single marble by the number of marbles: V_total = 33.49 mm^3/marble * 50 marbles = 1674.5 mm^3
The volume of the unused space in the container can be calculated by subtracting the volume of all the marbles from the total volume of the container: Unused volume = 4000 mm^3 - 1674.5 mm^3 = 2325.5 mm^3
Rounded to the nearest tenth, the unused space in the box is 2325.5 mm^3. Therefore, the correct answer is 2,325.3 mm^3.