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
2,325.3 mm3
2,325.3 mm cubed
33.5 mm3
33.5 mm cubed
1,674.7 mm3
1,674.7 mm cubed
3,900 mm3
To find the total volume occupied by the marbles, we first need to calculate the volume of a single marble. The formula for the volume of a sphere is given as V = (4/3)πr^3, where r is the radius of the sphere.
Given that the radius of each marble is 2 mm and using 3.14 as an approximation for π, the volume of a single marble can be calculated as:
V = (4/3) * 3.14 * (2^3) = 33.49 mm^3 (rounded to two decimal places)
To find the total volume occupied by the marbles, we can multiply the volume of a single marble by the number of marbles:
Total volume occupied by marbles = 33.49 mm^3 * 50 = 1674.5 mm^3 (rounded to one decimal place)
The volume of the container is given as 4000 mm^3.
To find the unused space in the box, we subtract the total volume occupied by the marbles from the volume of the container:
Unused space = Volume of the container - Total volume occupied by marbles = 4000 mm^3 - 1674.5 mm^3 = 2325.5 mm^3
Rounded to the nearest tenth, the unused space in the box is 2325.5 mm^3.
Therefore, the correct answer is:
2,325.3 mm^3