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
3,900 mm3
3,900 mm cubed
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
To find the volume of the marbles, we need to calculate the volume of a single marble and then multiply it by the number of marbles.
The volume of a sphere (marble) can be calculated using the formula:
V = (4/3) * pi * r^3
Given that the radius of each marble is 2 mm and using the approximation of pi as 3.14, we can calculate the volume of a single marble:
V = (4/3) * 3.14 * (2)^3
V = (4/3) * 3.14 * 8
V = 33.49333333 mm3
Now, to find the total volume of the marbles, we multiply the volume of a single marble by the number of marbles:
Total volume of marbles = 33.49333333 mm3/marble * 50 marbles
Total volume of marbles = 1674.6666665 mm3
To find the unused space in the container, we subtract the volume of the marbles from the total volume of the container:
Unused space = 4000 mm3 - 1674.6666665 mm3
Unused space = 2325.3333335 mm3
Rounded to the nearest tenth, the unused space in the box is 2325.3 mm3 or 2325.3 mm cubed.