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
1,674.7 mm3
1,674.7 mm cubed
3,900 mm3
3,900 mm cubed
2,325.3 mm3
To find the total volume occupied by 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)πr^3
We are given that the radius of each marble is 2 mm, so let's substitute this value into the formula:
V = (4/3)(3.14)(2^3)
V ≈ 33.4933333333 mm^3 (rounded to the nearest tenth)
Next, we can find the total volume occupied by the marbles by multiplying the volume of a single marble by the number of marbles:
Total volume occupied = 33.4933333333 mm^3 * 50 = 1674.66666667 mm^3 (rounded to the nearest tenth)
Finally, to find the unused space in the container, we subtract the total volume occupied by the marbles from the volume of the container:
Unused space = 4000 mm^3 - 1674.66666667 mm^3 = 2325.33333333 mm^3 (rounded to the nearest tenth)
Therefore, the unused space in the box is approximately 2325.3 mm^3.