Question

The volume of a container measures 4,000 mm^3 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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the marbles, we can use the formula for the volume of a sphere:

V = (4/3)πr^3

Where V is the volume and r is the radius of the sphere.

Plugging in the given radius of 2 mm, we get:

V = (4/3)(3.14)(2^3)
V = (4/3)(3.14)(8)
V ≈ 33.51 mm^3

Now, to find the total volume of all 50 marbles, we can multiply the volume of one marble by 50:

Total volume of marbles = 33.51 mm^3 * 50
Total volume of marbles ≈ 1675.5 mm^3

To find the unused space in the container, we subtract the volume of the marbles from the volume of the container:

Unused space = 4000 mm^3 - 1675.5 mm^3
Unused space ≈ 2324.5 mm^3

Rounding to the nearest tenth, the unused space is approximately 2324.5 mm^3.

So, the correct answer is:

2,325.3 mm^3