The volume of a container measures 4000 mm³, and contains 50 marbles. Each marble has a radius of 2 mm use 3.14 as an approximation for pie how much space is in the box unused round your answer to the nearest 10th

Answer 1

To find the space unused in the box, we need to subtract the volume occupied by the marbles from the total volume of the container.

First, we need to find the volume occupied by one marble. The formula for the volume of a sphere is V = (4/3) * π * r³, where r is the radius.

For a marble with a radius of 2 mm:
V = (4/3) * 3.14 * 2³
V ≈ 33.49 mm³

Next, we find the total volume occupied by all the marbles:
Total volume occupied = 33.49 mm³ * 50 marbles
Total volume occupied = 1674.5 mm³

Finally, we subtract the total volume occupied by the marbles from the total volume of the container:
Space unused = 4000 mm³ - 1674.5 mm³
Space unused ≈ 2325.5 mm³

Rounding to the nearest 10th, the space unused in the box is approximately 2325.5 mm³.