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 mm^3

33.5 mm^3

3,900 mm^3

2,325.3 mm^3

Answer 1

Volume of one marble = (4/3)πr^3 = (4/3)(3.14)(2^3) = (4/3)(3.14)(8) = 33.4933... mm^3
Volume of 50 marbles = 50 × 33.4933... ≈ 1674.6667 mm^3
Unused space = 4000 − 1674.6667 ≈ 2325.3333 → 2325.3 mm^3

Answer: 2,325.3 mm^3