Question

The volume container messures 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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of each marble can be calculated by the formula: V = (4/3)πr^3.

Using π as 3.14 and the radius of each marble as 2 mm, we have:
V = (4/3)(3.14)(2^3)
V ≈ (4/3)(3.14)(8)
V ≈ (4/3)(25.12)
V ≈ 33.49 mm³.

The total volume of all the marbles is calculated by multiplying the volume of each marble by the number of marbles:
Total volume = 33.49 mm³/marble * 50 marbles
Total volume ≈ 1674.5 mm³.

To find the unused space in the box, we subtract the total volume of the marbles from the volume of the container:
Unused space = 4000 mm³ - 1674.5 mm³
Unused space ≈ 2325.5 mm³.

Rounding the answer to the nearest tenth, the unused space in the box is approximately 2325.5 mm³. Answer: \boxed{2325.5}.