The volume of a container measures 4,000 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.(1 point)
Responses
33.5 mm3
33.5 mm cubed
1,674.7 mm3
1,674.7 mm cubed
2,325.3 mm3
2,325.3 mm cubed
3,900 mm3
First, let's calculate the total volume occupied by the marbles. The volume of each marble can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3. Given that the radius of each marble is 2 mm, we can calculate the volume of each marble:
V_marble = (4/3) * 3.14 * (2^3) = 33.49 mm^3
Since there are 50 marbles, the total volume occupied by the marbles is:
Total volume of marbles = V_marble * 50 = 33.49 mm^3 * 50 = 1674.5 mm^3 (rounded to the nearest tenth)
To find the unused space in the container, we subtract the total volume occupied by the marbles from the volume of the container:
Unused space = Volume of container - Total volume of marbles = 4000 mm^3 - 1674.5 mm^3 = 2325.5 mm^3 (rounded to the nearest tenth)
Therefore, the correct answer is "2,325.3 mm3" or "2,325.3 mm cubed".