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.

Answer 1

First, we need to find the total volume occupied by the marbles in the container.

Volume of a sphere = (4/3) * π * r^3
= (4/3) * 3.14 * 2^3
= (4/3) * 3.14 * 8
= 33.51 mm^3

Total volume occupied by 50 marbles = 50 * 33.51 = 1675.5 mm^3

Now, we subtract the total volume occupied by the marbles from the volume of the container to find the space unused.

Unused space = Total volume of the container - Total volume occupied by marbles
= 4000 - 1675.5
= 2324.5 mm^3

Therefore, the space unused in the box is 2324.5 mm^3.