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.
1. 2,325.3 mm^3
2. 3,900 mm^3
3. 33.5 mm^3
4. 1,674.7 mm^3
The volume of one marble can be calculated using the formula for the volume of a sphere: V = (4/3) * π * r^3. Substituting the given values, we have V = (4/3) * 3.14 * 2^3 = 33.51 mm^3 (rounded to the nearest hundredth).
To find the volume of all 50 marbles, we multiply the volume of one marble by the number of marbles: 33.51 mm^3/marble * 50 marbles = 1675.5 mm^3 (rounded to the nearest tenth).
The unused space in the box can be calculated by subtracting the volume of the marbles from the volume of the container: 4000 mm^3 - 1675.5 mm^3 = 2324.5 mm^3 (rounded to the nearest tenth).
Therefore, the space unused in the box is approximately 2,324.5 mm^3, which is closest to answer choice 1: 2,325.3 mm^3.