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 pi. How much space in the box is unused? Round your answer to the nearest tenth.
First, let's calculate the volume of 1 marble:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.
So, the volume of 1 marble is:
V = (4/3) * 3.14 * 2³
V = (4/3) * 3.14 * 8
V = 33.49333 mm³ (rounded to 5 decimal places)
Now, let's calculate the total volume of all the marbles:
Total volume of marbles = 50 marbles * 33.49333 mm³/marble
Total volume of marbles = 1674.6665 mm³
Now, let's find the unused space in the box:
Unused space = Total volume of the box - Total volume of marbles
Unused space = 4000 mm³ - 1674.6665 mm³
Unused space = 2325.3335 mm³
Rounded to the nearest tenth, the space unused in the box is approximately 2325.3 mm³.