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
2,325.3 mm3
2,325.3 mm cubed
1,674.7 mm3
1,674.7 mm cubed
3,900 mm3
2,325.3 mm3
2,325.3 mm cubed
To calculate the total volume occupied by the marbles, we first find the volume of one marble using the formula V = (4/3) * pi * r^3, where r is the radius of the marble:
V = (4/3) * 3.14 * 2^3
V = (4/3) * 3.14 * 8
V = 33.51 mm^3
Since there are 50 marbles, the total volume occupied by the marbles is:
50 * 33.51 = 1,675.5 mm^3
To find the unused space in the box, we subtract the volume of the marbles from the total volume of the container:
4000 - 1,675.5 = 2,324.5 mm^3
Rounded to the nearest tenth, the unused space in the box is 2,325.3 mm3.