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 3,900 mm^3
b 2,325.3 mm^3
c 1,674.7 mm^3
d 33.5 mm^3
The volume of each marble can be calculated using the formula for the volume of a sphere:
V = (4/3) * π * r^3
Plugging in the given radius of 2 mm and using an approximation of pi as 3.14, we get:
V = (4/3) * 3.14 * 2^3
V = 33.493333...
Since the given volume of the container is 4,000 mm^3, the total volume of all the marbles would be:
50 * 33.493333... = 1674.666666...
Rounding to the nearest tenth, the total volume of the marbles is approximately 1674.7 mm^3.
To find the unused space, we subtract this from the volume of the container:
4000 - 1674.7 ≈ 2325.3
Therefore, the answer is b) 2,325.3 mm^3.