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

2,325.3 mm3
2,325.3 mm cubed

3,900 mm3
3,900 mm cubed

1,674.7 mm3
1,674.7 mm cubed

33.5 mm3

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 mm^3 ≈ 2325.3 mm^3.

Answer: 2,325.3 mm^3.