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)Responses3,900 mm33,900 mm cubed2,325.3 mm32,325.3 mm cubed33.5 mm333.5 mm cubed1,674.7 mm3
The volume of the marbles can be calculated by using the formula for the volume of a sphere: V = (4/3)πr^3, where r is the radius.
V = (4/3) * 3.14 * 2^3
V = (4/3) * 3.14 * 8
V = 33.49 mm^3 per marble
Since there are 50 marbles, the total volume of the marbles is:
50 * 33.49 = 1674.5 mm^3
Subtracting this from the total volume of the container:
4000 - 1674.5 = 2325.5 mm^3
Rounded to the nearest tenth, the space unused in the box is 2325.5 mm^3. Answer: 2325.3 mm^3