Question

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

1,674.7 mm3
1,674.7 mm cubed

33.5 mm3
33.5 mm cubed

2,325.3 mm3
2,325.3 mm cubed

3,900 mm3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of 50 marbles, we first need to find the volume of one marble and then multiply it by 50. The formula to find the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.

Given that the radius of each marble is 2 mm, we can calculate the volume of one marble:

V = (4/3)π(2^3)
= (4/3)π(8)
= (32/3)π
≈ 33.5 mm^3 (rounded to the nearest tenth)

Now, since there are 50 marbles, the total volume for all the marbles is:

Total volume = 33.5 mm^3 * 50
≈ 1675 mm^3 (rounded to the nearest tenth)

Therefore, the unused space in the box is the total volume of the container minus the total volume of the marbles:

Unused space = 4000 mm^3 - 1675 mm^3
= 2325 mm^3

So, the space in the box that is unused is approximately 2,325.3 mm^3