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.
A. 2,325.3 mm^3
B. 33.5 mm^3
C. 3,900 mm^3
D. 1,674.7 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.
Total volume of 50 marbles = 50 × 33.4933... = 1674.6667 ≈ 1674.7 mm^3.
Unused space = 4000 − 1674.7 = 2325.3 mm^3.

Answer: A. 2,325.3 mm^3.